% This file was created with JabRef 2.10. % Encoding: UTF-8 @String { Send_Questions_Or_Comments_To = {vladik@utep.edu} } @Article{Achenie:2003:IGO, Title = {Interval Global Optimization in Solvent Design}, Author = {L. E. K. Achenie and M. Sinha}, Journal = {Reliable Computing}, Year = {2003}, Number = {5}, Pages = {317--338}, Volume = {9} } @Article{Acioly:1997:QMT, Title = {A Quasi-Metric Topology Compatible with Inclusion Monotonicity on Interval Space}, Author = {B. Acioly and B. Bedregal}, Journal = {Reliable Computing}, Year = {1997}, Number = {3}, Pages = {305--313}, Volume = {3} } @Article{Akhmerov:2005:IAG, Title = {Interval-Affine Gaussian Algorithm for Constrained Systems}, Author = {R. R. Akhmerov}, Journal = {Reliable Computing}, Year = {2005}, Number = {5}, Pages = {323--341}, Volume = {11} } @Article{Akritas:1995:MCS, Title = {Matrix computation of subresultant polynomial remainder sequences in integral domains}, Author = {A. G. Akritas and E. K. Akritas and G. I. Malaschonok}, Journal = {Reliable Computing}, Year = {1995}, Number = {4}, Pages = {375--382}, Volume = {1} } @Article{Akunova:1992:CCS, Title = {Construction of a comparison system for multivariate control processes with interval state matrix}, Author = {A. Akunova and T. A. Akunov and A. V. Ushakov}, Journal = {Interval Computations}, Year = {1992}, Number = {3}, Pages = {8--12} } @Article{Akyildiz:1993:NPI, Title = {No pathologies for interval {N}ewton's method}, Author = {Y. Akyildiz and M. I. Al-Suwaiyel}, Journal = {Interval Computations}, Year = {1993}, Number = {1}, Pages = {60--72} } @Article{Alefeld:2001:CSS, Title = {A Comment on the Shape of the Solution Set for Systems of Interval Linear Equations with Dependent Coefficients}, Author = {G. Alefeld and V. Kreinovich and G. Mayer and M. Huth}, Journal = {Reliable Computing}, Year = {2001}, Number = {3}, Pages = {275--277}, Volume = {7} } @Article{Alefeld:2005:ESS, Title = {Enclosing Solutions of Singular Interval Systems Iteratively}, Author = {G. Alefeld and G. Mayer}, Journal = {Reliable Computing}, Year = {2005}, Number = {3}, Pages = {165--190}, Volume = {11} } @Article{Alefeld:1994:CAE, Title = {A Computer Aided Existence and Uniqueness Proof for an Inverse Matrix Eigenvalue Problem}, Author = {G. Alefeld and G. Mayer}, Journal = {Interval Computations}, Year = {1994}, Number = {1}, Pages = {4--27} } @Article{Alefeld:2004:ESL, Title = {Enclosing Solutions of Linear Complementarity Problems for {H}-matrices}, Author = {G. Alefeld and Z. Wang and Z. Shen}, Journal = {Reliable Computing}, Year = {2004}, Number = {6}, Pages = {423--435}, Volume = {10} } @Article{Alliez:2000:RDP, Title = {Removing Degeneracies by Perturbing the Problem or Perturbing the World}, Author = {P. Alliez and O. Devillers and J. Snoeyink}, Journal = {Reliable Computing}, Year = {2000}, Number = {1}, Pages = {61--79}, Volume = {6} } @Article{Alt:2011:ASL, Title = {On the Accuracy of the Solution of Linear Problems on the {CELL} Processor}, Author = {Ren{\'{e}} Alt and Jean-Luc Lamotte and Svetoslav Markov}, Journal = {Reliable Computing}, Year = {2011}, Month = {May}, Number = {1}, Pages = {1--12}, Volume = {15} } @Article{Alvarado:1993:DSI, Title = {Direct Sparse Interval Hull Computations for Thin Non-{M}-Matrices}, Author = {F. L. Alvarado and Zian Wang}, Journal = {Interval Computations}, Year = {1993}, Number = {2}, Pages = {5--28} } @Article{Anguelov:1999:WFI, Title = {Wrapping Function of the Initial Value Problem for {ODE}: Applications}, Author = {R. Anguelov}, Journal = {Reliable Computing}, Year = {1999}, Number = {2}, Pages = {143--164}, Volume = {5} } @Article{Anguelov:1998:WEW, Title = {Wrapping Effect and Wrapping Function}, Author = {R. Anguelov and S. Markov}, Journal = {Reliable Computing}, Year = {1998}, Number = {4}, Pages = {311--330}, Volume = {4} } @Article{Anguelov:2006:SHC, Title = {The Set of Hausdorff Continuous Functions - The Largest Linear Space of Interval Functions}, Author = {R. Anguelov and S. Markov and B. Sendov}, Journal = {Reliable Computing}, Year = {2006}, Number = {4}, Pages = {337--363}, Volume = {12} } @Article{Anile:2004:MUS, Title = {Modeling Uncertain Sparse Data with Fuzzy {B}-splines}, Author = {A. M. Anile and S. Spinella}, Journal = {Reliable Computing}, Year = {2004}, Number = {5}, Pages = {335--355}, Volume = {10} } @Article{Ansary:2015:HOR, Title = {Higher Order Root Finding Algorithm using Interval Analysis}, Author = {Md. Abu Talhamainuddin Ansary and Geetanjali Panda}, Journal = {Reliable Computing}, Year = {2015}, Month = {Sep}, Number = {1}, Pages = {11--24}, Volume = {21} } @Article{Argaez:2011:SOS, Title = {Solving Overdetermined Systems in $l_{p}$ Quasi-Norms}, Author = {Miguel Arg{\'{a}}ez}, Journal = {Reliable Computing}, Year = {2011}, Month = {May}, Number = {1}, Pages = {13--25}, Volume = {15} } @Article{Argaez:2011:HAG, Title = {A Hybrid Algorithm for Global Optimization Problems}, Author = {Miguel Arg{\'{a}}ez and Leticia Vel{\'{a}}zquez and Carlos Quintero and Hector Klie and Mary Wheeler}, Journal = {Reliable Computing}, Year = {2011}, Month = {Jul}, Number = {3}, Pages = {230--241}, Volume = {15} } @Article{Armengol:2001:AMI, Title = {Application of Modal Intervals to the Generation of Error-Bounded Envelopes}, Author = {J. Armengol and J. Vehi and L. Trave-Massuyes and M. A. Sainz }, Journal = {Reliable Computing}, Year = {2001}, Number = {2}, Pages = {171--185}, Volume = {7} } @Article{Arndt:2007:ISP, Title = {On Interval Systems [x]=[A][x]+[b] and the Powers of Interval Matrices in Complex Interval Arithmetics}, Author = {H.-R. Arndt}, Journal = {Reliable Computing}, Year = {2007}, Number = {3}, Pages = {245--259}, Volume = {13} } @Article{Arndt:2005:SIS, Title = {On the Solutions of the Interval System [x]=[A][x]+[b]}, Author = {H.-R. Arndt and G. Mayer}, Journal = {Reliable Computing}, Year = {2005}, Number = {2}, Pages = {87--103}, Volume = {11} } @Article{Auer:2013:UVM, Title = {Uses of Verified Methods for Solving Non--Smooth Initial Value Problems}, Author = {Ekaterina Auer and Stefan Kiel}, Journal = {Reliable Computing}, Year = {2013}, Month = {Dec}, Number = {2}, Pages = {156--175}, Volume = {19} } @Article{Bela:2012:RRA, Title = {Real Root Approximation Using Fat Spheres}, Author = {Szilvia B{\'{e}}la and Bert J{\"{u}}ttler}, Journal = {Reliable Computing}, Year = {2012}, Month = {Dec}, Number = {2}, Pages = {72--96}, Volume = {17} } @Article{Bunger:2014:NBS, Title = {A Note on the Boundary Shape of Matrix Polytope Products}, Author = {Florian B{\"u}nger}, Journal = {Reliable Computing}, Year = {2014}, Month = {Oct}, Number = {1}, Pages = {73--88}, Volume = {20} } @Article{Bunger:2016:SNC, Title = {A Short Note on the Convexity of Interval Matrix--Vector Products}, Author = {Florian B{\"u}nger and Siegfried M. Rump}, Journal = {Reliable Computing}, Year = {2016}, Month = {Jun}, Number = {1}, Pages = {74--79}, Volume = {21} } @Article{Babichev:1993:UNA, Title = {{UniCalc}, a Novel Approach to Solving Systems of Algebraic Equations}, Author = {A. B. Babichev and O. B. Kadyrova and T. P. Kashevarova and A. S. Leshchenko and A. L. Semenov}, Journal = {Interval Computations}, Year = {1993}, Number = {2}, Pages = {29--47} } @Article{Babichev:1992:UTS, Title = {{UniCalc} as a tool for solving problems with inaccurate and sub-definite data}, Author = {A. B. Babichev and O. B. Kadyrova and T. P. Kashevarova and A. L. Semenov}, Journal = {Interval Computations}, Year = {1992}, Number = {3}, Pages = {13--16} } @Article{Backeljauw:2005:CCP, Title = {A Constructive Criticism of the {C}/{C}++ Proposal for Complex Arithmetic}, Author = {F. Backeljauw and A. Cuyt}, Journal = {Reliable Computing}, Year = {2005}, Number = {4}, Pages = {313--319}, Volume = {11} } @Article{Baker:1998:UAT, Title = {Universal Approximation Theorem for Interval Neural Networks}, Author = {M. R. Baker and R. B. Patil}, Journal = {Reliable Computing}, Year = {1998}, Number = {3}, Pages = {235--239}, Volume = {4} } @Article{Balaji:1995:AIN, Title = {Application of interval Newton's method to chemical engineering problems}, Author = {G. V. Balaji and J. D. Seader}, Journal = {Reliable Computing}, Year = {1995}, Number = {3}, Pages = {215--224}, Volume = {1} } @Article{Beaumont:2001:LIT, Title = {Linear Interval Tolerance Problem and Linear Programming Techniques}, Author = {O. Beaumont and B. Philippe}, Journal = {Reliable Computing}, Year = {2001}, Number = {6}, Pages = {433--447}, Volume = {7} } @Article{Beckermann:2000:ECR, Title = {Effective Computation of Rational Approximants and Interpolants}, Author = {B. Beckermann and G. Labahn}, Journal = {Reliable Computing}, Year = {2000}, Number = {4}, Pages = {365--390}, Volume = {6} } @Article{Beelitz:2006:ETS, Title = {Efficient Task Scheduling in the Parallel Result-Verifying Solution of Nonlinear Systems}, Author = {T. Beelitz and B. Lang and C. H. Bischof}, Journal = {Reliable Computing}, Year = {2006}, Number = {2}, Pages = {141--151}, Volume = {12} } @Article{Beelitz:2010:CCT, Title = {Closing the Case $t = 3$ for 3-{D} Spherical $t$-Designs Using a Result-Verifying Nonlinear Solver}, Author = {Thomas Beelitz and Bruno Lang and Peer Ueberholz and Paul Willems}, Journal = {Reliable Computing}, Year = {2010}, Month = {Jun}, Number = {1}, Pages = {66--77}, Volume = {14} } @Article{Beltran:1998:ASP, Title = {Algorithms That Still Produce a Solution (Maybe Not Optimal) Even When Interrupted: {S}hary's Idea Justified}, Author = {M. Beltran and G. Castillo and V. Kreinovich}, Journal = {Reliable Computing}, Year = {1998}, Number = {1}, Pages = {39--53}, Volume = {4} } @Article{Benhamou:1997:AGN, Title = {Automatic Generation of Numerical Redundancies for Non-Linear Constraint Solving}, Author = {F. Benhamou and L. Granvilliers}, Journal = {Reliable Computing}, Year = {1997}, Number = {3}, Pages = {335--344}, Volume = {3} } @Article{Berleant:2002:RCS, Title = {Reliable Computing: Special Issue on Dependable Reasoning about Uncertainty}, Author = {D. Berleant}, Journal = {Reliable Computing}, Year = {2002}, Number = {2}, Pages = {175--176}, Volume = {8} } @Article{Berleant:1993:AVR, Title = {Automatically Verified Reasoning with Both Intervals and Probability Density Functions}, Author = {D. Berleant}, Journal = {Interval Computations}, Year = {1993}, Number = {2}, Pages = {48--70} } @Article{Berleant:1998:STA, Title = {A Software Tool for Automatically Verified Operations on Intervals and Probability Distributions}, Author = {D. Berleant and H. Cheng}, Journal = {Reliable Computing}, Year = {1998}, Number = {1}, Pages = {71--82}, Volume = {4} } @Article{Berleant:2003:DHU, Title = {Dependable Handling of Uncertainty}, Author = {D. Berleant and M.-P. Cheong and C. Chu and Y. Guan and A. Kamal and G. Sheble and S. Ferson and J. F. Peters}, Journal = {Reliable Computing}, Year = {2003}, Number = {6}, Pages = {407--418}, Volume = {9} } @Article{Berleant:1998:BRA, Title = {Bounding the Results of Arithmetic Operations on Random Variables of Unknown Dependency Using Intervals}, Author = {D. Berleant and C. Goodman-Strauss}, Journal = {Reliable Computing}, Year = {1998}, Number = {2}, Pages = {147--165}, Volume = {4} } @Article{Berleant:2003:STD, Title = {{Statool}: A Tool for Distribution Envelope Determination ({DEnv}), an Interval-Based Algorithm for Arithmetic on Random Variables}, Author = {D. Berleant and L. Xie and J. Zhang}, Journal = {Reliable Computing}, Year = {2003}, Number = {2}, Pages = {91--108}, Volume = {9} } @Article{Berleant:2004:UPC, Title = {Using {P}earson Correlation to Improve Envelopes around the Distributions of Functions}, Author = {D. Berleant and J. Zhang}, Journal = {Reliable Computing}, Year = {2004}, Number = {2}, Pages = {139--161}, Volume = {10} } @Article{Berleant:2007:UIL, Title = {Unimodality, Independence Lead to NP-Hardness of Interval Probability Problems}, Author = {D. J. Berleant and O. Kosheleva and V. Kreinovich and H. T. Nguyen}, Journal = {Reliable Computing}, Year = {2007}, Number = {3}, Pages = {261--282}, Volume = {13} } @Article{Berthelot:1997:CSE, Title = {Computing on Sequences of Embedded Intervals}, Author = {D. Berthelot and M. Daumas}, Journal = {Reliable Computing}, Year = {1997}, Number = {3}, Pages = {219--227}, Volume = {3} } @Article{Berz:2001:VHO, Title = {Verified High-Order Inversion of Functional Dependencies and Interval Newton Methods}, Author = {M. Berz and J. Hoefkens}, Journal = {Reliable Computing}, Year = {2001}, Number = {5}, Pages = {379--398}, Volume = {7} } @Article{Berz:1998:CAT, Title = {Computation and Application of Taylor Polynomials with Interval Remainder Bounds}, Author = {M. Berz and G. Hoffstaetter}, Journal = {Reliable Computing}, Year = {1998}, Number = {1}, Pages = {83--97}, Volume = {4} } @Article{Berz:1994:EBL, Title = {Exact Bounds on the Long Term Stability of Weakly Nonlinear Systems Applied to the Design of Large Storage Rings}, Author = {M. Berz and G. Hoffstaetter}, Journal = {Interval Computations}, Year = {1994}, Number = {2}, Pages = {68--89} } @Article{Berz:1999:NMH, Title = {New Methods for High-Dimensional Verified Quadrature}, Author = {M. Berz and K. Makino}, Journal = {Reliable Computing}, Year = {1999}, Number = {1}, Pages = {13--22}, Volume = {5} } @Article{Berz:1998:VIO, Title = {Verified Integration of {ODE}s and Flows Using Differential Algebraic Methods on High-Order {T}aylor Models}, Author = {M. Berz and K. Makino}, Journal = {Reliable Computing}, Year = {1998}, Number = {4}, Pages = {361--369}, Volume = {4} } @Article{Birdie:1998:UIA, Title = {The Use of Interval Analysis in Hydrologic Systems}, Author = {T. R. Birdie and K. S. Surana}, Journal = {Reliable Computing}, Year = {1998}, Number = {3}, Pages = {269--281}, Volume = {4} } @Article{Bliek:1997:FEP, Title = {Fast Evaluation of Partial Derivatives and Interval Slopes}, Author = {C. Bliek}, Journal = {Reliable Computing}, Year = {1997}, Number = {3}, Pages = {259--268}, Volume = {3} } @Article{Blomquist:2011:SCC, Title = {Staggered Correction Computations with Enhanced Accuracy and Extremely Wide Exponent Range}, Author = {Frithjof Blomquist}, Journal = {Reliable Computing}, Year = {2011}, Month = {May}, Number = {1}, Pages = {26--35}, Volume = {15} } @Article{Blomquist:1992:IID, Title = {Interval inclusions for {D}awson's integral}, Author = {F. Blomquist}, Journal = {Interval Computations}, Year = {1992}, Number = {3}, Pages = {17--26} } @Article{Bochkov:1992:AEZ, Title = {Algorithm for experimental zero-order optimization for plant with bounded amplitude errors}, Author = {A. F. Bochkov and L. A. Yakovleva}, Journal = {Interval Computations}, Year = {1992}, Number = {3}, Pages = {27--30} } @Article{Bochkov:1992:IND, Title = {Identification of nonlinear dynamic objects using interval experimental data}, Author = {A. F. Bochkov and N. V. Zung}, Journal = {Interval Computations}, Year = {1992}, Number = {3}, Pages = {31--37} } @Article{Bohlender:2011:DAO, Title = {Definition of the Arithmetic Operations and Comparison Relations for an Interval Arithmetic}, Author = {Gerd Bohlender and Ulrich Kulisch}, Journal = {Reliable Computing}, Year = {2011}, Month = {May}, Number = {1}, Pages = {36--42}, Volume = {15} } @Article{Bondia:2004:AFI, Title = {Application of Functional Intervals to the Response Evaluation of Linear Time-Invariant Systems with Fuzzy Input}, Author = {J. Bondia and J. Pico}, Journal = {Reliable Computing}, Year = {2004}, Number = {5}, Pages = {369--387}, Volume = {10} } @Article{Brito:1998:IIW, Title = {Interval + Image = Wavelet: For Image Processing under Interval Uncertainty, Wavelets Are Optimal}, Author = {A. E. Brito and O. Kosheleva}, Journal = {Reliable Computing}, Year = {1998}, Number = {3}, Pages = {291--301}, Volume = {4} } @Article{Campos:1996:MTI, Title = {Mechanising the theory of intervals using {OBJ3}}, Author = {M. A. Campos and A. C. A. Sampaio and A. H. F. Brainer}, Journal = {Reliable Computing}, Year = {1996}, Number = {2}, Pages = {97--102}, Volume = {2} } @Article{Candau:2006:CIA, Title = {Complex Interval Arithmetic Using Polar Form}, Author = {Y. Candau and T. Raissi and N. Ramdani and L. Ibos}, Journal = {Reliable Computing}, Year = {2006}, Number = {1}, Pages = {1--20}, Volume = {12} } @Article{Caprani:1993:URV, Title = {Use of a Real-Valued Local Minimum in Parallel Interval Global Optimization}, Author = {O. Caprani and B. Godthaab and K. Madsen}, Journal = {Interval Computations}, Year = {1993}, Number = {2}, Pages = {71--82} } @Article{Caprani:1997:RER, Title = {Robust and Efficient Ray Intersection of Implicit Surfaces}, Author = {O. Caprani and L. Hvidegaard and M. Mortensen and T. Schneider}, Journal = {Reliable Computing}, Year = {2000}, Number = {1}, Pages = {9--21}, Volume = {6} } @Article{Caprani:1997:ETA, Title = {Existence Test for Asynchronous Interval Iteration}, Author = {O. Caprani and K. Madsen and O. Stauning}, Journal = {Reliable Computing}, Year = {1997}, Number = {3}, Pages = {269--275}, Volume = {3} } @Article{Casado:2000:IBB, Title = {Interval Branch and Bound Algorithm for Finding the First-Zero-Crossing-Point in One-Dimensional Functions}, Author = {L. G. Casado and I. F. Garcia and Y. D. Sergeyev}, Journal = {Reliable Computing}, Year = {2000}, Number = {2}, Pages = {179--191}, Volume = {6} } @Article{Ceberio:2004:FMI, Title = {Fast Multiplication of Interval Matrices (Interval Version of {S}trassen's Algorithm)}, Author = {M. Ceberio and V. Kreinovich}, Journal = {Reliable Computing}, Year = {2004}, Number = {3}, Pages = {241--243}, Volume = {10} } @Article{Cervesato:1993:NBE, Title = {On the Non-monotonic Behaviour of Event Calculus for Deriving Maximal Time Intervals}, Author = {I. Cervesato and A. Montanari and A. Provetti}, Journal = {Interval Computations}, Year = {1993}, Number = {2}, Pages = {83--119} } @Article{Chabert:2007:EHB, Title = {Extension of the Hansen-Bliek Method to Right-Quantified Linear Systems}, Author = {G. Chabert and A. Goldsztejn}, Journal = {Reliable Computing}, Year = {2007}, Number = {4}, Pages = {325--349}, Volume = {13} } @Article{Chabert:2007:CPI, Title = {Computing the Pessimism of Inclusion Functions}, Author = {G. Chabert and L. Jaulin}, Journal = {Reliable Computing}, Year = {2007}, Number = {6}, Pages = {489--504}, Volume = {13} } @Article{Chee:1997:CVB, Title = {Computing the Value of a Boolean Expression with Interval Inputs is {NP}-Hard}, Author = {L. S. Chee}, Journal = {Reliable Computing}, Year = {1997}, Number = {2}, Pages = {155--172}, Volume = {3} } @Article{Cheu:2011:TPO, Title = {Towards the Possibility of Objective Interval Uncertainty in Physics}, Author = {Darrell Cheu and Luc Longpr{\'{e}}}, Journal = {Reliable Computing}, Year = {2011}, Month = {May}, Number = {1}, Pages = {43--46}, Volume = {15} } @Article{Chiu:2002:EIL, Title = {Efficient Interval Linear Equality Solving in Constraint Logic Programming}, Author = {C.-K. Chiu and J. H.-M. Lee}, Journal = {Reliable Computing}, Year = {2002}, Number = {2}, Pages = {139--174}, Volume = {8} } @Article{Christiansen:1994:IMC, Title = {Interval Methods and Condition Numbers of Linear Algebraic Systems}, Author = {S. Christiansen}, Journal = {Interval Computations}, Year = {1994}, Number = {4}, Pages = {4--27} } @Article{Claudio:1992:OTA, Title = {An order-theoretical approach to interval analysis}, Author = {D. M. Claudio and M. H. Escardo and B. R. T. Franciosi}, Journal = {Interval Computations}, Year = {1992}, Number = {3}, Pages = {38--45} } @Article{Collavizzal:1999:CPC, Title = {Comparing Partial Consistencies}, Author = {H. Collavizza and F. Delobel and M. Rueher}, Journal = {Reliable Computing}, Year = {1999}, Number = {3}, Pages = {213--228}, Volume = {5} } @Article{Connell:1993:EIA, Title = {An Experimental Interval Arithmetic Package in {M}aple}, Author = {A. E. Connell and R. M. Corless}, Journal = {Interval Computations}, Year = {1993}, Number = {2}, Pages = {120--134} } @Article{Cooke:1995:IIH, Title = {An informal introduction to a high level language with applications to interval mathematics}, Author = {D. E. Cooke}, Journal = {Reliable Computing}, Year = {1995}, Number = {1}, Pages = {65--76}, Volume = {1} } @Article{Corliss:2007:FRA, Title = {Formulation for Reliable Analysis of Structural Frames}, Author = {G. Corliss and C. Foley and R. B. Kearfott}, Journal = {Reliable Computing}, Year = {2007}, Number = {2}, Pages = {125--147}, Volume = {13} } @Article{Corsaro:2010:AAI, Title = {Archetypal Analysis of Interval Data}, Author = {Stefania Corsaro and Marina Marino}, Journal = {Reliable Computing}, Year = {2010}, Month = {Jun}, Number = {1}, Pages = {105--116}, Volume = {14} } @Article{Cooke:1999:CEB, Title = {Computing Exact Bounds on Elements of an Inverse Interval Matrix is {NP}-Hard}, Author = {G. E. Coxson}, Journal = {Reliable Computing}, Year = {1999}, Number = {2}, Pages = {137--142}, Volume = {5} } @Article{Crespo:2012:UFT, Title = {A Unifying Framework to Uncertainty Quantification of Polynomial Systems Subject to Aleatory and Epistemic Uncertainty}, Author = {Luis G. Crespo and Daniel P. Giesy and Sean P. Kenny}, Journal = {Reliable Computing}, Year = {2012}, Month = {Dec}, Number = {2}, Pages = {97--127}, Volume = {17} } @Article{Csendes:2003:NEN, Title = {Numerical Experiences with a New Generalized Subinterval Selection Criterion for Interval Global Optimization}, Author = {T. Csendes}, Journal = {Reliable Computing}, Year = {2003}, Number = {2}, Pages = {109--125}, Volume = {9} } @Article{Dang:2012:RAP, Title = {Reachability Analysis for Polynomial Dynamical Systems Using the {B}ernstein Expansion}, Author = {Thao Dang and Romain Testylier}, Journal = {Reliable Computing}, Year = {2012}, Month = {Dec}, Number = {2}, Pages = {128--152}, Volume = {17} } @Article{Danqing:1999:SUS, Title = {Solving Underdetermined Systems with Interval Methods}, Author = {Z. Danqing and L. Weiguo and S. Zuhe}, Journal = {Reliable Computing}, Year = {1999}, Number = {1}, Pages = {23--33}, Volume = {5} } @Article{Dantsin:2006:PVI, Title = {Population Variance under Interval Uncertainty: A New Algorithm}, Author = {E. Dantsin and V. Kreinovich and A. Wolpert and G. Xiang}, Journal = {Reliable Computing}, Year = {2006}, Number = {4}, Pages = {273--280}, Volume = {12} } @Article{Daumas:1994:RFP, Title = {Rounding of Floating Point Intervals}, Author = {M. Daumas and D. W. Matula}, Journal = {Interval Computations}, Year = {1994}, Number = {4}, Pages = {28--45} } @Article{Daumas:1994:TUT, Title = {Towards a User Transparent Interval Arithmetic}, Author = {M. Daumas and Ch. Mazenc and J.-M. Muller}, Journal = {Interval Computations}, Year = {1994}, Number = {4}, Pages = {46--63} } @Article{Davidenkoff:1992:APL, Title = {{ACRITH-XSC}: A programming language for scientific/engineering computation}, Author = {A. Davidenkoff}, Journal = {Interval Computations}, Year = {1992}, Number = {2}, Pages = {72--82} } @Article{Davis:1998:NAL, Title = {A New Application of Local Minima of Interval Functions: Interval-Valued Fuzzy Control}, Author = {C. Davis}, Journal = {Reliable Computing}, Year = {1998}, Number = {1}, Pages = {99--101}, Volume = {4} } @Article{Visser:2012:INA, Title = {Intersplines: {A} New Approach to Globally Optimal Multivariate Splines Using Interval Analysis}, Author = {Coen C. {de Visser} and Eric-Jan {van Kampen} and Q. Ping Chu and J. A. Mulder}, Journal = {Reliable Computing}, Year = {2012}, Month = {Dec}, Number = {2}, Pages = {153--191}, Volume = {17} } @Article{Weerdt:2012:PIF, Title = {Polynomial Inclusion Functions}, Author = {E. {de Weerdt} and E. {van Kampen} and Q. P. Chu and J. A. Mulder}, Journal = {Reliable Computing}, Year = {2012}, Month = {Nov}, Number = {1}, Pages = {283--307}, Volume = {16} } @Article{Delanoue:2007:GHT, Title = {Guaranteeing the Homotopy Type of a Set Defined by Non-Linear Inequalities}, Author = {N. Delanoue and L. Jaulin and B. Cottenceau}, Journal = {Reliable Computing}, Year = {2007}, Number = {5}, Pages = {381--398}, Volume = {13} } @Article{Delgado:2012:OBR, Title = {Optimality of {B}ernstein Representations for Computational Purposes}, Author = {Jorge Delgado and Juan Manuel Pe{\~{n}}a}, Journal = {Reliable Computing}, Year = {2012}, Month = {Dec}, Number = {1}, Pages = {1--10}, Volume = {17} } @Article{Demchenko:1992:STN, Title = {Syntesis of transport networks structures under conditions of uncertain initial information}, Author = {A. I. Demchenko and B. V. Peltsverger and O. V. Khavronin}, Journal = {Interval Computations}, Year = {1992}, Number = {3}, Pages = {46--49} } @Article{Dennis:1998:IOC, Title = {Intervals and the Origins of Calculus}, Author = {D. Dennis and V. Kreinovich and S. M. Rump}, Journal = {Reliable Computing}, Year = {1998}, Number = {2}, Pages = {191--197}, Volume = {4} } @Article{Diep:2011:SCS, Title = {Solving and Certifying the Solution of a Linear System}, Author = {Nguyen Hong Diep and Nathalie Revol}, Journal = {Reliable Computing}, Year = {2011}, Month = {Jun}, Number = {2}, Pages = {120--131}, Volume = {15} } @Article{Dimitrova:1999:VCF, Title = {Verified Computation of Fast Decreasing Polynomials}, Author = {N. S. Dimitrova and S. M. Markov}, Journal = {Interval Computations}, Year = {1999}, Number = {3}, Pages = {229--240}, Volume = {5} } @Article{Dimitrova:1994:VNT, Title = {On Validated {N}ewton Type Method for Nonlinear Equations}, Author = {N. S. Dimitrova and S. M. Markov}, Journal = {Interval Computations}, Year = {1994}, Number = {2}, Pages = {27--51} } @Article{Dimuro:2000:CSR, Title = {A Coherence Space of Rational Intervals for a Construction of {IR}}, Author = {G. P. Dimuro and A. C. da R. Costa and D. M. Claudio}, Journal = {Reliable Computing}, Year = {2000}, Number = {2}, Pages = {139--178}, Volume = {6} } @Article{Sandretto:2016:VEI, Title = {Validated Explicit and Implicit {R}unge--{K}utta Methods}, Author = {Julien Alexandre {dit Sandretto} and Alexandre Chapoutot}, Journal = {Reliable Computing}, Year = {2016}, Month = {Jul}, Number = {1}, Pages = {79--103}, Volume = {22} } @Article{Sandretto:2016:VSD, Title = {Validated Simulation of Differential Algebraic Equations with {R}unge--{K}utta Methods}, Author = {Julien Alexandre {dit Sandretto} and Alexandre Chapoutot}, Journal = {Reliable Computing}, Year = {2016}, Month = {Jul}, Number = {1}, Pages = {56--77}, Volume = {22} } @Article{Diverio:1996:EVP, Title = {Errors in vector processing and the library {libavi.a}}, Author = {T. A. Diverio and U. A. Fernandes and D. M. Claudio}, Journal = {Reliable Computing}, Year = {1996}, Number = {2}, Pages = {103--110}, Volume = {2} } @Article{Djanybekov:2006:IHM, Title = {Interval Householder Method for Complex Linear Systems}, Author = {B. S. Djanybekov}, Journal = {Reliable Computing}, Year = {2006}, Number = {1}, Pages = {35--43}, Volume = {12} } @Article{Do:2004:SAR, Title = {Spigot Algorithm and Reliable Computation of Natural Logarithm}, Author = {D.-K. Do}, Journal = {Reliable Computing}, Year = {2004}, Number = {6}, Pages = {489--500}, Volume = {10} } @Article{Do:2001:SAR, Title = {Spigot Algorithm and Root Computing}, Author = {D.-K. Do}, Journal = {Reliable Computing}, Year = {2001}, Number = {3}, Pages = {247--273}, Volume = {7} } @Article{Dobner:2002:KST, Title = {Kernel-Splitting Technique for Enclosing the Solution of {F}redholm Equations of the First Kind}, Author = {H.-J. Dobner}, Journal = {Reliable Computing}, Year = {2002}, Number = {6}, Pages = {469--479}, Volume = {8} } @Article{Dobner:2001:KI, Title = {On Kernel Inclusions}, Author = {H.-J. Dobner}, Journal = {Reliable Computing}, Year = {2001}, Number = {1}, Pages = {29--39}, Volume = {7} } @Article{Dobner:1996:BHQ, Title = {Bounds of high quality for first kind {V}olterra integral equations}, Author = {H.-J. Dobner}, Journal = {Reliable Computing}, Year = {1996}, Number = {1}, Pages = {35--46}, Volume = {2} } @Article{Dobner:1997:ACM, Title = {Attacking a conjecture in mathematical physics by combining methods of computational analysis and scientific computing}, Author = {H.-J. Dobner and S. Ritter}, Journal = {Reliable Computing}, Year = {1997}, Number = {3}, Pages = {287--295}, Volume = {3} } @Article{Dobronets:1997:TSM, Title = {Two-sided Multigrid Method for Elliptic Boundary Value Problems}, Author = {B. S. Dobronets}, Journal = {Reliable Computing}, Year = {1997}, Number = {3}, Pages = {297--303}, Volume = {3} } @Article{Dobronets:1995:NMU, Title = {Numerical methods using defects}, Author = {B. S. Dobronets}, Journal = {Reliable Computing}, Year = {1995}, Number = {4}, Pages = {383--392}, Volume = {1} } @Article{Dobronets:1992:IMB, Title = {Interval methods based on a posteriori estimates}, Author = {B. S. Dobronets}, Journal = {Interval Computations}, Year = {1992}, Number = {3}, Pages = {50--55} } @Article{Dobronets:1992:STS, Title = {On some two-sided methods for solving systems of ordinary differential equations}, Author = {B. S. Dobronets}, Journal = {Interval Computations}, Year = {1992}, Number = {1}, Pages = {6--21} } @Article{Dobronets:2014:NPA, Title = {Numerical Probabilistic Analysis under Aleatory and Epistemic Uncertainty}, Author = {Boris S. Dobronets and Olga A. Popova}, Journal = {Reliable Computing}, Year = {2014}, Month = {Apr}, Number = {3}, Pages = {274--289}, Volume = {19} } @Article{Dobronets:1991:IES, Title = {On interval extension of some classes of functions}, Author = {B. S. Dobronets and V. I. Senashov}, Journal = {Interval Computations}, Year = {1991}, Number = {1}, Pages = {54--58} } @Article{Dolgov:2005:DIG, Title = {Developing Interval Global Optimization Algorithms on the Basis of Branch-and-Bound and Constraint Propagation Methods}, Author = {Y. G. Dolgov}, Journal = {Reliable Computing}, Year = {2005}, Number = {5}, Pages = {343--358}, Volume = {11} } @Article{Dombrovskii:2014:MPC, Title = {Model Predictive Control for Linear Systems with Interval and Stochastic Uncertainties}, Author = {Vladimir V. Dombrovskii and Elena V. Chausova}, Journal = {Reliable Computing}, Year = {2014}, Month = {Jun}, Number = {4}, Pages = {351--360}, Volume = {19} } @Article{Doser:1998:EUG, Title = {Estimating Uncertainties for Geophysical Tomography}, Author = {D. I. Doser and K. D. Crain and M. R. Baker and V. Kreinovich and M. C. Gerstenberger}, Journal = {Reliable Computing}, Year = {1998}, Number = {3}, Pages = {241--268}, Volume = {4} } @Article{Dubois:2004:PPT, Title = {Probability-Possibility Transformations, Triangular Fuzzy Sets, and Probabilistic Inequalities}, Author = {D. Dubois and L. Foulloy and G. Mauris and H. Prade}, Journal = {Reliable Computing}, Year = {2004}, Number = {4}, Pages = {273--297}, Volume = {10} } @Article{Dugarova:1992:AIM, Title = {An algorithm of interval matrix asymptotic stability testing}, Author = {I. V. Dugarova}, Journal = {Interval Computations}, Year = {1992}, Number = {3}, Pages = {56--62} } @Article{Dyllong:1999:ADC, Title = {An Accurate Distance-Calculation Algorithm for Convex Polyhedra}, Author = {E. Dyllong and W. Luther and W. Otten}, Journal = {Reliable Computing}, Year = {1999}, Number = {3}, Pages = {241--253}, Volume = {5} } @Article{Dyllong:2006:MGO, Title = {Modelling Geometric Objects and Tolerances with Intervals: Data Exchange with ISO Standard STEP}, Author = {E. Dyllong and W. Luther and H. Traczinski}, Journal = {Reliable Computing}, Year = {2006}, Number = {4}, Pages = {293--302}, Volume = {12} } @Article{Eberhart:2015:HPN, Title = {High Performance Numerical Validation using Stochastic Arithmetic}, Author = {Pac{\^o}me Eberhart and Julien Brajard and Pierre Fortin and Fabienne J{\'e}z{\'e}quel}, Journal = {Reliable Computing}, Year = {2015}, Month = {Dec}, Number = {1}, Pages = {35--52}, Volume = {21} } @Article{Edmonson:2000:IMS, Title = {Interval Methods for Sinusoidal Parameter Estimation: A Comparative Analysis}, Author = {W. W. Edmonson and W. H. Lee and J. M. M. Anderson}, Journal = {Reliable Computing}, Year = {2000}, Number = {3}, Pages = {321--336}, Volume = {6} } @Article{Eick:1996:RAL, Title = {Robust algorithms that locate local extrema of a function of one variable from interval measurement results: A remark}, Author = {C. Eick and K. Villaverde}, Journal = {Reliable Computing}, Year = {1996}, Number = {3}, Pages = {213--218}, Volume = {2} } @Article{Ely:1993:VSP, Title = {The {VPI} Software Package for Variable Precision Interval Arithmetic}, Author = {J. S. Ely}, Journal = {Interval Computations}, Year = {1993}, Number = {2}, Pages = {135--154} } @Article{Ely:2000:CDT, Title = {Correct {D}elaunay Triangulation in the Presence of Inexact Inputs and Arithmetic}, Author = {J. S. Ely and A. P. Leclerc}, Journal = {Reliable Computing}, Year = {2000}, Number = {1}, Pages = {23--38}, Volume = {6} } @Article{Emden:2004:SDI, Title = {On the Significance of Digits in Interval Notation}, Author = {M. H. van Emden}, Journal = {Reliable Computing}, Year = {2004}, Number = {1}, Pages = {45--58}, Volume = {10} } @Article{Enszer:2011:VSP, Title = {Verified Solution and Propagation of Uncertainty in Physiological Models}, Author = {Joshua A. Enszer and Mark A. Stadtherr}, Journal = {Reliable Computing}, Year = {2011}, Month = {Jul}, Number = {3}, Pages = {168--178}, Volume = {15} } @Article{Erascu:2013:SOQ, Title = {The {S}ecant--{N}ewton Map is Optimal Among Contracting Quadratic Maps for Square Root Computation}, Author = {M{\={a}}d{\={a}}lina Era{\c{s}}cu and Hoon Hong}, Journal = {Reliable Computing}, Year = {2013}, Month = {May}, Number = {1}, Pages = {73--81}, Volume = {18} } @Article{Eriksson:1995:PIM, Title = {A parallel interval method implementation for global optimization using dynamic load balancing}, Author = {J. Eriksson and P. Lindstrom}, Journal = {Reliable Computing}, Year = {1995}, Number = {1}, Pages = {77--92}, Volume = {1} } @Article{Ermakov:1994:SSO, Title = {Solving Systems of Ordinary Differential Equations Using {A}dams' Interpolation Method with Guaranteed Accuracy}, Author = {O. B. Ermakov}, Journal = {Interval Computations}, Year = {1994}, Number = {1}, Pages = {90--95} } @Article{Ermakov:1992:TSM, Title = {Two-sided method for solving system of ordinary differential equations with automatic determination of guaranteed estimates}, Author = {O. B. Ermakov}, Journal = {Interval Computations}, Year = {1992}, Number = {3}, Pages = {63--69} } @Article{Ershov:2005:IML, Title = {Interval Mathematical Library Based on Chebyshev and Taylor Series Expansion}, Author = {A. G. Ershov and T. P. Kashevarova}, Journal = {Reliable Computing}, Year = {2005}, Number = {5}, Pages = {359--367}, Volume = {11} } @Article{Evtushenko:1992:OPS, Title = {Optimization problems for static plants under uncertainty conditions}, Author = {T. V. Evtushenko}, Journal = {Interval Computations}, Year = {1992}, Number = {3}, Pages = {70--74} } @Article{Fang:2003:OBF, Title = {Optimal Bicentered Form}, Author = {Y. Fang}, Journal = {Reliable Computing}, Year = {2003}, Number = {4}, Pages = {291--302}, Volume = {9} } @Article{Farouki:2002:EMP, Title = {Exact {M}inkowski Products of N Complex Disks}, Author = {R. T. Farouki and H. Pottmann}, Journal = {Reliable Computing}, Year = {2002}, Number = {1}, Pages = {43--66}, Volume = {8} } @Article{Faudot:2007:NRA, Title = {A New Robust Algorithm to Trace Curves}, Author = {D. Faudot and D. Michelucci}, Journal = {Reliable Computing}, Year = {2007}, Number = {4}, Pages = {309--324}, Volume = {13} } @Article{Ferregut:1996:FEE, Title = {Fast error estimates for indirect measurements: applications to pavement engineering}, Author = {C. Ferregut and S. Nazarian and K. Vennalaganti and C.-C. Chang and Vladik Kreinovich}, Journal = {Reliable Computing}, Year = {1996}, Number = {3}, Pages = {219--228}, Volume = {2} } @Article{Ferson:2005:EBF, Title = {Exact Bounds on Finite Populations of Interval Data}, Author = {S. Ferson and L. Ginzburg and V. Kreinovich and L. Longpre and M. Aviles}, Journal = {Reliable Computing}, Year = {2005}, Number = {3}, Pages = {207--233}, Volume = {11} } @Article{Filippov:1992:EEE, Title = {Ellipsoidal error estimates for {A}dams method}, Author = {A. F. Filippov}, Journal = {Interval Computations}, Year = {1992}, Number = {3}, Pages = {75--79} } @Article{Filippov:1992:EES, Title = {Ellipsoidal estimates for a solution of a system of differential equations}, Author = {A. F. Filippov}, Journal = {Interval Computations}, Year = {1992}, Number = {2}, Pages = {6--17} } @Article{Foufou:2012:BBA, Title = {The {B}ernstein Basis and its Applications in Solving Geometric Constraint Systems}, Author = {Sebti Foufou and Dominique Michelucci}, Journal = {Reliable Computing}, Year = {2012}, Month = {Dec}, Number = {2}, Pages = {192--208}, Volume = {17} } @Article{Fournier:2000:RIS, Title = {Rational Interpolation from Stochastic Data: A New {F}roissart's Phenomenon}, Author = {J.-D. Fournier and M. Pindor}, Journal = {Reliable Computing}, Year = {2000}, Number = {4}, Pages = {391--409}, Volume = {6} } @Article{Friesen:1995:ORI, Title = {{O}ckham's razor in interval identification}, Author = {B. H. Friesen and V. Kreinovich}, Journal = {Reliable Computing}, Year = {1995}, Number = {3}, Pages = {225--238}, Volume = {1} } @Article{Frommer:1999:VEB, Title = {Verified Error Bounds for Linear Systems Through the {L}anczos Process}, Author = {A. Frommer and A. Weinberg}, Journal = {Reliable Computing}, Year = {1999}, Number = {3}, Pages = {255--267}, Volume = {5} } @Article{Funge:1998:RKS, Title = {Representing Knowledge within the Situation Calculus Using Interval-Valued Epistemic Fluents}, Author = {J. Funge}, Journal = {Reliable Computing}, Year = {1998}, Number = {1}, Pages = {35--61}, Volume = {5} } @Article{Gabaldon:1998:EOO, Title = {Exclusive {OR} Operation That Leads to the Narrowest Intervals}, Author = {A. Gabaldon and H. T. Nguyen}, Journal = {Reliable Computing}, Year = {1998}, Number = {3}, Pages = {303--306}, Volume = {4} } @Article{Garajova:2016:SVN, Title = {Solving and Visualizing Nonlinear Set Inversion Problems}, Author = {Elif Garajov{\'{a}} and Martin Me{\v{c}}iar}, Journal = {Reliable Computing}, Year = {2016}, Month = {Jul}, Number = {1}, Pages = {104--115}, Volume = {22} } @Article{Gardenes:2001:MI, Title = {Modal Intervals}, Author = {E. Gardenes and M. A. Sainz and L. Jorba and R. Calm and R. Estela and H. Mielgo and A. Trepat}, Journal = {Reliable Computing}, Year = {2001}, Number = {2}, Pages = {77--111}, Volume = {7} } @Article{Garloff:2000:ABE, Title = {Application of {B}ernstein Expansion to the Solution of Control Problems}, Author = {J. Garloff}, Journal = {Reliable Computing}, Year = {2000}, Number = {3}, Pages = {303--320}, Volume = {6} } @Article{Garloff:1993:BA, Title = {The {B}ernstein Algorithm}, Author = {J. Garloff}, Journal = {Interval Computations}, Year = {1993}, Number = {2}, Pages = {154--168} } @Article{Garloff:2007:GPS, Title = {Guaranteed Parameter Set Estimation for Exponential Sums: The Three-Terms Case}, Author = {J. Garloff and I. Idriss and A. P. Smith}, Journal = {Reliable Computing}, Year = {2007}, Number = {4}, Pages = {351--359}, Volume = {13} } @Article{Garloff:2010:KLN, Title = {{Karl L. E. Nickel} (1924 -- 2009)}, Author = {J{\"u}rgen Garloff}, Journal = {Reliable Computing}, Year = {2010}, Month = {Jun}, Number = {1}, Pages = {61--65}, Volume = {14} } @Article{Garloff:2016:SCM, Title = {A Survey of Classes of Matrices Possessing the Interval Property and Related Properties}, Author = {J{\"u}rgen Garloff and Mohammad Adm and Jihad Titi}, Journal = {Reliable Computing}, Year = {2016}, Month = {Jan}, Number = {1}, Pages = {1--14}, Volume = {22} } @Article{Gatilov:2013:EAS, Title = {Efficient Angle Summation Algorithm for Point Inclusion Test and Its Robustness}, Author = {Stepan Yu. Gatilov}, Journal = {Reliable Computing}, Year = {2013}, Month = {Aug}, Number = {1}, Pages = {1--25}, Volume = {19} } @Article{Gavrilova:2000:ECD, Title = {Exact Computation of {D}elaunay and Power Triangulations}, Author = {M. Gavrilova and H. Ratschek and J. G. Rokne}, Journal = {Reliable Computing}, Year = {2000}, Number = {1}, Pages = {39--60}, Volume = {6} } @Article{Gioia:2016:CAP, Title = {Capital Asset Pricing Model Using Regression Methods for Interval--Valued Variables}, Author = {Federica Gioia}, Journal = {Reliable Computing}, Year = {2016}, Month = {May}, Number = {1}, Pages = {53--73}, Volume = {21} } @Article{Glazunov:1992:IEC, Title = {On interval extensions of computer algebra systems}, Author = {N. M. Glazunov}, Journal = {Interval Computations}, Year = {1992}, Number = {3}, Pages = {80--87} } @Article{Goldsztejn:2012:MIO, Title = {Modal Intervals Revisited, Part 1: {A} Generalized Interval Natural Extension}, Author = {Alexandre Goldsztejn}, Journal = {Reliable Computing}, Year = {2012}, Month = {Oct}, Number = {1}, Pages = {130--183}, Volume = {16} } @Article{Goldsztejn:2012:MIT, Title = {Modal Intervals Revisited, Part 2: {A} Generalized Interval Mean Value Extension}, Author = {Alexandre Goldsztejn}, Journal = {Reliable Computing}, Year = {2012}, Month = {Oct}, Number = {1}, Pages = {184--209}, Volume = {16} } @Article{Goldsztejn:2005:RPP, Title = {A Right-Preconditioning Process for the Formal-Algebraic Approach to Inner and Outer Estimation of AE-Solution Sets}, Author = {A. Goldsztejn}, Journal = {Reliable Computing}, Year = {2005}, Number = {6}, Pages = {443--478}, Volume = {11} } @Article{Goldsztejn:2016:PMH, Title = {A Parallelotope Method for Hybrid System Simulation}, Author = {Alexandre Goldsztejn and Daisuke Ishii}, Journal = {Reliable Computing}, Year = {2016}, Month = {Jul}, Number = {1}, Pages = {163--185}, Volume = {23} } @Article{Goldsztejn:2010:IAR, Title = {Inner Approximation of the Range of Vector-Valued Functions}, Author = {Alexandre Goldsztejn and Luc Jaulin}, Journal = {Reliable Computing}, Year = {2010}, Month = {Jun}, Number = {1}, Pages = {1--23}, Volume = {14} } @Article{Goldsztejn:2011:CCP, Title = {Capabilities of Constraint Programming in Safe Global Optimization}, Author = {Alexandre Goldsztejn and Yahia Lebbah and Claude Michel and Michel Rueher}, Journal = {Reliable Computing}, Year = {2011}, Month = {May}, Number = {1}, Pages = {47--59}, Volume = {15} } @Article{Goldsztejn:2014:EIM, Title = {On the Exponentiation of Interval Matrices}, Author = {Alexandre Goldsztejn and Arnold Neumaier}, Journal = {Reliable Computing}, Year = {2014}, Month = {Oct}, Number = {1}, Pages = {53--72}, Volume = {20} } @Article{Gonzalez:1998:IHD, Title = {Intervals Help to Design an Imaging System}, Author = {G. Gonzalez}, Journal = {Reliable Computing}, Year = {1998}, Number = {1}, Pages = {103--104}, Volume = {4} } @Article{Graillat:2016:DCN, Title = {Dynamical Control of {N}ewton's Method for Multiple Roots of Polynomials}, Author = {Stef Graillat and Fabienne J{\'e}z{\'e}quel and Moustadrani Sa{\"\i}d Ibrahim}, Journal = {Reliable Computing}, Year = {2016}, Month = {Oct}, Number = {1}, Pages = {117--139}, Volume = {21} } @Article{Granvilliers:2001:CIC, Title = {On the Combination of Interval Constraint Solvers}, Author = {L. Granvilliers}, Journal = {Reliable Computing}, Year = {2001}, Number = {6}, Pages = {467--483}, Volume = {7} } @Article{Graves-Morris:2000:RLT, Title = {Reliability of {L}anczos-Type Product Methods from Perturbation Theory}, Author = {P. R. Graves-Morris}, Journal = {Reliable Computing}, Year = {2000}, Number = {4}, Pages = {411--428}, Volume = {6} } @Article{WolffVonGudenberg:2002:IAM, Title = {Interval Arithmetic on Multimedia Architectures}, Author = {J. Wolff von Gudenberg}, Journal = {Reliable Computing}, Year = {2002}, Number = {4}, Pages = {307--312}, Volume = {8} } @Article{WolffVonGudenberg:1995:DPL, Title = {Design of a parallel linear algebra library for verified computation}, Author = {J. Wolff von Gudenberg}, Journal = {Reliable Computing}, Year = {1995}, Number = {4}, Pages = {411--420}, Volume = {1} } @Article{WolffVonGudenberg:1995:PAL, Title = {Parallel accurate linear algebra subroutines}, Author = {J. Wolff von Gudenberg}, Journal = {Reliable Computing}, Year = {1995}, Number = {2}, Pages = {189--200}, Volume = {1} } @Article{WolffVonGudenberg:1992:PLS, Title = {Programming language support for scientific computation}, Author = {J. Wolff von Gudenberg}, Journal = {Interval Computations}, Year = {1992}, Number = {4}, Pages = {116--126} } @Article{Hager:1993:SLS, Title = {Solving Large Systems of Nonlinear Constraints with Application to Data Modeling}, Author = {G. D. Hager}, Journal = {Interval Computations}, Year = {1993}, Number = {2}, Pages = {169--200} } @Article{Hajagos:2007:IMC, Title = {Interval Monte Carlo as an Alternative to Second-Order Sampling for Estimating Ecological Risk}, Author = {J. G. Hajagos}, Journal = {Reliable Computing}, Year = {2007}, Number = {1}, Pages = {71--81}, Volume = {13} } @Article{Hammer:1991:PNL, Title = {{PASCAL-XSC}: A new language for scientific computing}, Author = {R. Hammer and M. Neaga and D. Ratz and D. Shiryaev}, Journal = {Interval Computations}, Year = {1991}, Number = {2}, Pages = {47--81} } @Article{Hansen:2015:RMO, Title = {{Ramon Moore}: {S}hort Biography and Recollections from Close Associates}, Author = {Eldon Hansen and Bill Walster and Sergey P. Shary and George Corliss and Luc Jaulin and Ulrich Kulisch and Michael Cloud and Louis Rall}, Journal = {Reliable Computing}, Year = {2015}, Month = {Apr}, Number = {1}, Pages = {2--14}, Volume = {23} } @Article{Hansen:2006:MIN, Title = {A Multidimensional Interval Newton Method}, Author = {E. R. Hansen}, Journal = {Reliable Computing}, Year = {2006}, Number = {4}, Pages = {253--272}, Volume = {12} } @Article{Hansen:2006:SIC, Title = {Sharpening Interval Computations}, Author = {E. R. Hansen}, Journal = {Reliable Computing}, Year = {2006}, Number = {1}, Pages = {21--34}, Volume = {12} } @Article{Hansen:2005:TRI, Title = {A Theorem on Regularity of Interval Matrices}, Author = {E. R. Hansen}, Journal = {Reliable Computing}, Year = {2005}, Number = {6}, Pages = {495--497}, Volume = {11} } @Article{Hansen:2000:HPI, Title = {The Hull of Preconditioned Interval Linear Equations}, Author = {E. R. Hansen}, Journal = {Reliable Computing}, Year = {2000}, Number = {2}, Pages = {95--103}, Volume = {6} } @Article{Hansen:2000:R, Title = {Reminiscences}, Author = {E. R. Hansen}, Journal = {Reliable Computing}, Year = {2000}, Number = {2}, Pages = {225}, Volume = {6} } @Article{Hansen:1993:CZF, Title = {Computing Zeros of Functions Using Generalized Interval Arithmetic}, Author = {E. R. Hansen}, Journal = {Interval Computations}, Year = {1993}, Number = {3}, Pages = {3--28} } @Article{Hansen:1993:SIC, Title = {Sharpness in Interval Computations}, Author = {E. R. Hansen}, Journal = {Reliable Computing}, Year = {1993}, Number = {1}, Pages = {17--29}, Volume = {3} } @Article{Hansen:2006:SOS, Title = {Solving Overdetermined Systems of Interval Linear Equations}, Author = {E. R. Hansen and G. W. Walster}, Journal = {Reliable Computing}, Year = {2006}, Number = {3}, Pages = {239--243}, Volume = {12} } @Article{Hansen:2002:SBI, Title = {Sharp Bounds on Interval Polynomial Roots}, Author = {E. R. Hansen and G. W. Walster}, Journal = {Reliable Computing}, Year = {2002}, Number = {2}, Pages = {115--122}, Volume = {8} } @Article{Harlow:2012:MRP, Title = {Mapped Regular Pavings}, Author = {Jennifer Harlow and Raazesh Sainudiin and Warwick Tucker}, Journal = {Reliable Computing}, Year = {2012}, Month = {Nov}, Number = {1}, Pages = {252--282}, Volume = {16} } @Article{Hashemi:2013:NIM, Title = {A Non--Induced Interval Matrix Norm}, Author = {Benham Hashemi and Hanieh Tavakolipour}, Journal = {Reliable Computing}, Year = {2013}, Month = {Nov}, Number = {1}, Pages = {144--146}, Volume = {18} } @Article{Hattangady:2011:BFP, Title = {Block Floating Point Interval {ALU} for Digital Signal Processing}, Author = {Sandeep Hattangady and William Edmonson and Winser Alexander}, Journal = {Reliable Computing}, Year = {2011}, Month = {Jun}, Number = {2}, Pages = {69--80}, Volume = {15} } @Article{Heindl:2016:GTR, Title = {Generalizations of Theorems of {R}ohn and {V}rahatis}, Author = {Gerd Heindl}, Journal = {Reliable Computing}, Year = {2016}, Month = {Sep}, Number = {1}, Pages = {109--116}, Volume = {21} } @Article{Heindl:1999:HGF, Title = {How to Guarantee Finite Termination of Verifying Global Optimization Codes}, Author = {G. Heindl}, Journal = {Reliable Computing}, Year = {1999}, Number = {1}, Pages = {63--68}, Volume = {5} } @Article{Heindl:1999:RIH, Title = {A Representation of the Interval Hull of a Tolerance Polyhedron Describing Inclusions of Function Values and Slopes}, Author = {G. Heindl}, Journal = {Reliable Computing}, Year = {1999}, Number = {3}, Pages = {269--278}, Volume = {5} } @Article{Heindl:1997:HCI, Title = {How to Compute Interval Inclusions of Geodetic Coordinates from Interval Inclusions of Cartesian Coordinates}, Author = {G. Heindl}, Journal = {Reliable Computing}, Year = {1997}, Number = {4}, Pages = {421--435}, Volume = {3} } @Article{Heindl:1998:SLI, Title = {Solving Linear Interval Systems Is {NP}-Hard Even If We Exclude Overflow and Underflow}, Author = {G. Heindl and V. Kreinovich and A. V. Lakeyev}, Journal = {Reliable Computing}, Year = {1998}, Number = {4}, Pages = {383--388}, Volume = {4} } @Article{Heindl:2002:CIM, Title = {In Case of Interval (or More General) Uncertainty, No Algorithm Can Choose the Simplest Representative}, Author = {G. Heindl and V. Kreinovich and M. Rifqi}, Journal = {Reliable Computing}, Year = {2002}, Number = {3}, Pages = {213--227}, Volume = {8} } @Article{Henrisken:1992:PAG, Title = {Parallel algorithms for global optimization}, Author = {T. Henriksen and K. Madsen}, Journal = {Interval Computations}, Year = {1992}, Number = {3}, Pages = {88--95} } @Article{Herlocker:1995:AGD, Title = {An automatic and guaranteed determination of the number of roots of an analytic function interior to a simple closed curve in the complex plane}, Author = {J. Herlocker and J. Ely}, Journal = {Reliable Computing}, Year = {1995}, Number = {3}, Pages = {239--250}, Volume = {1} } @Article{Herrero:2012:EIS, Title = {An Efficient Implementation of the {SIVIA} Algorithm in a High--Level Numerical Programming Language}, Author = {Pau Herrero and Pantelis Georgiou and Christofer Toumazou and Beno{\^{i}}t Delaunay and Luc Jaulin}, Journal = {Reliable Computing}, Year = {2012}, Month = {Oct}, Number = {1}, Pages = {239--251}, Volume = {16} } @Article{Herrero:2005:QSI, Title = {Quantified Set Inversion Algorithm with Applications to Control}, Author = {P. Herrero and M. A. Sainz and J. Vehi and L. Jaulin}, Journal = {Reliable Computing}, Year = {2005}, Number = {5}, Pages = {369--382}, Volume = {11} } @Article{Hertling:2001:LUT, Title = {A Limitation for Underestimation via Twin Arithmetic}, Author = {P. Hertling}, Journal = {Reliable Computing}, Year = {2001}, Number = {2}, Pages = {157--169}, Volume = {7} } @Article{Herzberger:1991:TAB, Title = {On two algorithms for bounding the inverses of an interval matrix}, Author = {J. Herzberger and D. Bethke}, Journal = {Interval Computations}, Year = {1991}, Number = {1}, Pages = {44--53} } @Article{Heuveline:1996:CAT, Title = {Chebyshev acceleration techniques for large complex non {H}ermitian eigenvalue problems}, Author = {V. Heuveline and M. Sadkane}, Journal = {Reliable Computing}, Year = {1996}, Number = {2}, Pages = {111--118}, Volume = {2} } @Article{Hickey:2000:ICP, Title = {Interval Constraint Plotting for Interactive Visual Exploration of Implicitly Defined Relations}, Author = {T. J. Hickey and Z. Qiu and M. H. van Emden}, Journal = {Reliable Computing}, Year = {2000}, Number = {1}, Pages = {81--92}, Volume = {6} } @Article{Hladik:2010:SSC, Title = {Solution Sets of Complex Linear Interval Systems of Equations}, Author = {Milan Hlad{\'{i}}k}, Journal = {Reliable Computing}, Year = {2010}, Month = {Jun}, Number = {1}, Pages = {78--87}, Volume = {14} } @Article{Hladik:2011:ESM, Title = {An Eigenvalue Symmetric Matrix Contractor}, Author = {Milan Hlad{\'{i}}k and Luc Jaulin}, Journal = {Reliable Computing}, Year = {2011}, Month = {Oct}, Number = {1}, Pages = {27--37}, Volume = {16} } @Article{Hladik:2007:SSC, Title = {Solution Set Characterization of Linear Interval Systems with a Specific Dependence Structure}, Author = {M. Hladik}, Journal = {Reliable Computing}, Year = {2007}, Number = {4}, Pages = {361--374}, Volume = {13} } @Article{Hoefkens:2002:VIC, Title = {Verification of Invertibility of Complicated Functions over Large Domains}, Author = {J. Hoefkens and M. Berz}, Journal = {Reliable Computing}, Year = {2002}, Number = {1}, Pages = {67--82}, Volume = {8} } @Article{Hoefkens:2003:CWE, Title = {Controlling the Wrapping Effect in the Solution of {ODE}s for Asteroids}, Author = {J. Hoefkens and M. Berz and K. Makino}, Journal = {Reliable Computing}, Year = {2003}, Number = {1}, Pages = {21--41}, Volume = {9} } @Article{Hofschuster:2000:MFS, Title = {Mathematical Function Software on the Web - Are Such Codes Useful for Verification Algorithms?}, Author = {W. Hofschuster and W. Kraemer}, Journal = {Reliable Computing}, Year = {2000}, Number = {2}, Pages = {207--218}, Volume = {6} } @Article{Hofschuster:1996:COA, Title = {A Computer Oriented Approach to Get Sharp Reliable Error Bounds}, Author = {W. Hofschuster and W. Kraemer}, Journal = {Reliable Computing}, Year = {1996}, Number = {3}, Pages = {239--248}, Volume = {3} } @Article{Holzmann:1996:NCG, Title = {{N}ewton's constant of gravitation and verified numerical quadrature}, Author = {O. Holzmann and B. Lang and H. Schuett}, Journal = {Reliable Computing}, Year = {1996}, Number = {3}, Pages = {229--240}, Volume = {2} } @Article{Horacek:2013:CEO, Title = {Computing Enclosures of Overdetermined Interval Linear Systems}, Author = {J. Hor{\'a}{\v{c}}ek and M. Hlad{\'\i}k}, Journal = {Reliable Computing}, Year = {2013}, Month = {Nov}, Number = {2}, Pages = {142--155}, Volume = {19} } @Article{Horowitz:2003:CBP, Title = {Computation of Bounds on Population Parameters When the Data Are Incomplete}, Author = {J. L. Horowitz and C. F. Manski and M. Ponomareva and J. Stoye }, Journal = {Reliable Computing}, Year = {2003}, Number = {6}, Pages = {419--440}, Volume = {9} } @Article{Hu:1998:IPI, Title = {An Interval Polynomial Interpolation Problem and Its {L}agrange Solution}, Author = {C. Hu and A. Cardenas and S. Hoogendoorn and P. Sepulveda Jr.}, Journal = {Reliable Computing}, Year = {1998}, Number = {1}, Pages = {27--38}, Volume = {4} } @Article{Hu:1995:GIS, Title = {A general iterative sparse linear solver and its parallelization for interval {N}ewton methods}, Author = {C. Hu and A. Frolov and R. B. Kearfott and Q. Yang}, Journal = {Reliable Computing}, Year = {1995}, Number = {3}, Pages = {251--264}, Volume = {1} } @Article{Hu:2007:AIM, Title = {An Application of Interval Methods to Stock Market Forecasting}, Author = {C. Hu and L. T. He}, Journal = {Reliable Computing}, Year = {2007}, Number = {5}, Pages = {423--434}, Volume = {13} } @Article{Hu:1993:BRS, Title = {On Bounding the Range of Some Elementary Functions in {FORTRAN-77}}, Author = {C. Hu and R. B. Kearfott and A. Awad}, Journal = {Interval Computations}, Year = {1993}, Number = {3}, Pages = {29--40} } @Article{Hu:1995:OIC, Title = {Optimizing {INTBIS} on the {CRAY} {Y}-{MP}}, Author = {C. Hu and J. Sheldon and R. B. Kearfott and Q. Yang}, Journal = {Reliable Computing}, Year = {1995}, Number = {3}, Pages = {265--274}, Volume = {1} } @Article{Hu:1998:ROP, Title = {Reliable Optimal Production Control with {C}obb-{D}ouglas Model}, Author = {Z. H. Hu}, Journal = {Reliable Computing}, Year = {1998}, Number = {1}, Pages = {63--69}, Volume = {4} } @Article{Hungerbuehler:2000:CBC, Title = {Computation of the {B}ernstein Coefficients on Subdivided Triangles}, Author = {R. Hungerbuehler and J. Garloff}, Journal = {Reliable Computing}, Year = {2000}, Number = {2}, Pages = {115--121}, Volume = {6} } @Article{Hungerbuehler:1998:BRB, Title = {Bounds for the Range of a Bivariate Polynomial over a Triangle}, Author = {R. Hungerbuehler and J. Garloff}, Journal = {Reliable Computing}, Year = {1998}, Number = {1}, Pages = {3--13}, Volume = {4} } @Article{Huyer:2004:IAR, Title = {Integral Approximation of Rays and Verification of Feasibility}, Author = {W. Huyer and A. Neumaier}, Journal = {Reliable Computing}, Year = {2004}, Number = {3}, Pages = {195--207}, Volume = {10} } @Article{Ida:2004:SPS, Title = {Solutions for the Portfolio Selection Problem with Interval and Fuzzy Coefficients}, Author = {M. Ida}, Journal = {Reliable Computing}, Year = {2004}, Number = {5}, Pages = {389--400}, Volume = {10} } @Article{Inuiguchi:2004:FLP, Title = {Fuzzy Linear Programming with Interactive Uncertain Parameters}, Author = {M. Inuiguchi and T. Tanino}, Journal = {Reliable Computing}, Year = {2004}, Number = {5}, Pages = {357--367}, Volume = {10} } @Article{Ivlev:2007:ESI, Title = {Exponential Stability of Interval Dynamical Systems with Quadratic Nonlinearity}, Author = {R. S. Ivlev and S. P. Sokolova}, Journal = {Reliable Computing}, Year = {2007}, Number = {3}, Pages = {283--291}, Volume = {13} } @Article{Iwaarden:1993:ADA, Title = {Automatic Differentiation Applied to Unconstrained Nonlinear Optimization with Result Verification}, Author = {R. Van Iwaarden}, Journal = {Interval Computations}, Year = {1993}, Number = {3}, Pages = {41--60} } @Article{Jager:1995:CME, Title = {A combined method for enclosing all solutions of nonlinear systems of polynomial equations}, Author = {C. Jager and D. Ratz}, Journal = {Reliable Computing}, Year = {1995}, Number = {1}, Pages = {41--64}, Volume = {1} } @Article{Jansson:1998:NHR, Title = {An {NP}-Hardness Result for Nonlinear System}, Author = {C. Jansson}, Journal = {Reliable Computing}, Year = {1998}, Number = {4}, Pages = {345--350}, Volume = {4} } @Article{Jaulin:2016:IOS, Title = {Inner and Outer Set--Membership State Estimation}, Author = {Luc Jaulin}, Journal = {Reliable Computing}, Year = {2016}, Month = {Jun}, Number = {1}, Pages = {47--55}, Volume = {22} } @Article{Jaulin:2014:OAA, Title = {Outer Approximation of Attractors Using an Interval Quantization}, Author = {Luc Jaulin}, Journal = {Reliable Computing}, Year = {2014}, Month = {Apr}, Number = {3}, Pages = {261--273}, Volume = {19} } @Article{Jaulin:2001:PPU, Title = {Path Planning Using Intervals and Graphs}, Author = {L. Jaulin}, Journal = {Reliable Computing}, Year = {2001}, Number = {1}, Pages = {1--15}, Volume = {7} } @Article{Jaulin:2001:RMP, Title = {Reliable Minimax Parameter Estimation}, Author = {L. Jaulin}, Journal = {Reliable Computing}, Year = {2001}, Number = {3}, Pages = {231--246}, Volume = {7} } @Article{Jaulin:1999:EDE, Title = {Estimation of Discrete-Event Systems Using Interval Computation}, Author = {L. Jaulin and J.-L. Boimond and L. Hardouin}, Journal = {Reliable Computing}, Year = {1999}, Number = {2}, Pages = {165--173}, Volume = {5} } @Article{Jaulin:2016:BAD, Title = {Bisectable Abstract Domains for the Resolution of Equations Involving Complex Numbers}, Author = {Luc Jaulin and B. Desrochers and D. Mass{\'{e}}}, Journal = {Reliable Computing}, Year = {2016}, Month = {Jul}, Number = {1}, Pages = {35--46}, Volume = {23} } @Article{Jaulin:2005:COI, Title = {Contracting Optimally an Interval Matrix without Loosing Any Positive Semi-Definite Matrix Is a Tractable Problem}, Author = {L. Jaulin and D. Henrion}, Journal = {Reliable Computing}, Year = {2005}, Number = {1}, Pages = {1--17}, Volume = {11} } @Article{Jaulin:2004:SCN, Title = {Set Computation for Nonlinear Control}, Author = {L. Jaulin and S. Ratschan and L. Hardouin}, Journal = {Reliable Computing}, Year = {2004}, Number = {1}, Pages = {1--26}, Volume = {10} } @Article{Jaulin:1993:GNP, Title = {Guaranteed Nonlinear Parameter Estimation via Interval Computations}, Author = {L. Jaulin and E. Walter}, Journal = {Interval Computations}, Year = {1993}, Number = {3}, Pages = {61--75} } @Article{Jiang:2013:AVF, Title = {Accurate, Validated and Fast Evaluation of {B}{\'{e}}zier Tensor Product Surfaces}, Author = {Hao Jiang and Housen Li and Lizhi Cheng and Roberto Barrio and Canbin Hu and Xiangke Liao}, Journal = {Reliable Computing}, Year = {2013}, Month = {May}, Number = {1}, Pages = {55--72}, Volume = {18} } @Article{Johnson:2002:IIM, Title = {Intervals of Inverse {M}-matrices}, Author = {C. R. Johnson and R. L. Smith}, Journal = {Reliable Computing}, Year = {2002}, Number = {3}, Pages = {239--243}, Volume = {8} } @Article{Johnson:2006:HUD, Title = {Handling Uncertainty in the Development and Design of Chemical Processes}, Author = {D. B. Johnson and I. D. L. Bogle}, Journal = {Reliable Computing}, Year = {2006}, Number = {6}, Pages = {409--426}, Volume = {12} } @Article{Just:2012:SSE, Title = {A Success--Guided Selection of Expanded Systems for Result--Verifying Nonlinear Solvers}, Author = {Elke Just and Bruno Lang}, Journal = {Reliable Computing}, Year = {2012}, Month = {Mar}, Number = {1}, Pages = {73--83}, Volume = {16} } @Article{Kai:2000:HRF, Title = {Hybrid Rational Function Approximation and Its Accuracy Analysis}, Author = {H. Kai and M.-T. Noda}, Journal = {Reliable Computing}, Year = {2000}, Number = {4}, Pages = {429--438}, Volume = {6} } @Article{Kalovics:1999:SNC, Title = {Solving Nonlinear Constrained Minimization Problems with a New Interval Valued Function}, Author = {F. Kalovics}, Journal = {Reliable Computing}, Year = {1999}, Number = {4}, Pages = {395--406}, Volume = {5} } @Article{Kalovics:1997:FGM, Title = {Finding Global Minima of Maximum Functions by Using Exclusion Functions without Derivatives}, Author = {F. Kalovics and G. Meszaros}, Journal = {Reliable Computing}, Year = {1997}, Number = {4}, Pages = {381--399}, Volume = {3} } @Article{Kapitanski:2011:DRC, Title = {Dynamics with a Range of Choice}, Author = {Lev Kapitanski and Sanja {\v{Z}}ivanovi{\v{c}}}, Journal = {Reliable Computing}, Year = {2011}, Month = {Jul}, Number = {4}, Pages = {290--299}, Volume = {15} } @Article{Karcanias:2000:NCL, Title = {Numerical Computation of the Least Common Multiple of a Set of Polynomials}, Author = {N. Karcanias and M. Mitrouli}, Journal = {Reliable Computing}, Year = {2000}, Number = {4}, Pages = {439--457}, Volume = {6} } @Article{Karmakar:2012:CSD, Title = {A Comparative Study of Different Order Relations of Intervals}, Author = {Samiran Karmakar and A. K. Bhunia}, Journal = {Reliable Computing}, Year = {2012}, Month = {Jan}, Number = {1}, Pages = {38--72}, Volume = {16} } @Article{Kearfott:200:EOI, Title = {Errata and Opinion to: \emph{An Interval Entropy Penalty Method for Nonlinear Global Optimization}, by Zhenyu Huang, Reliable Computing 4 (1) (1998)}, Author = {R. B. Kearfott}, Journal = {Reliable Computing}, Year = {2005}, Number = {2}, Pages = {163--164}, Volume = {11} } @Article{Kearfott:2005:VCS, Title = {Validated Constraint Solving - Practicalities, Pitfalls, and New Developments}, Author = {R. B. Kearfott}, Journal = {Reliable Computing}, Year = {2005}, Number = {5}, Pages = {383--391}, Volume = {11} } @Article{Kearfott:2003:CWG, Title = {{COCOS'02}: A Workshop on Global Constrained Optimization and Constraint Satisfaction}, Author = {R. B. Kearfott}, Journal = {Reliable Computing}, Year = {2003}, Number = {1}, Pages = {81--87}, Volume = {9} } @Article{Kearfott:2002:EUV, Title = {On Existence and Uniqueness Verification for Non-Smooth Functions}, Author = {R. B. Kearfott}, Journal = {Reliable Computing}, Year = {2002}, Number = {4}, Pages = {267--282}, Volume = {8} } @Article{Kearfott:2001:ESN, Title = {An Example of Singularity in Nonlinear Systems}, Author = {R. B. Kearfott}, Journal = {Reliable Computing}, Year = {2001}, Number = {5}, Pages = {425--429}, Volume = {7} } @Article{Kearfott:1992:IPF, Title = {{INTLIB}: A portable {F}ortran-77 elementary function library}, Author = {R. B. Kearfott and M. Dawande and K. Du and C. Hu}, Journal = {Interval Computations}, Year = {1992}, Number = {3}, Pages = {96--105} } @Article{Kearfott:1991:RPI, Title = {A review of preconditioners for the interval {G}auss-{S}eidel method}, Author = {R. B. Kearfott and Chenyi Hu and M. Novoa III}, Journal = {Interval Computations}, Year = {1991}, Number = {1}, Pages = {59--85} } @Article{Kearfott:1993:PSH, Title = {A preconditioner selection heuristic for efficient iteration with decomposition of arithmetic expressions for nonlinear algebraic systems}, Author = {R. B. Kearfott and Xiaofa Shi}, Journal = {Interval Computations}, Year = {1993}, Number = {1}, Pages = {15--33} } @Article{Kearfott:2002:SPT, Title = {Symbolic Preconditioning with {T}aylor Models: Some Examples}, Author = {R. B. Kearfott and G. W. Walster}, Journal = {Reliable Computing}, Year = {2002}, Number = {6}, Pages = {453--468}, Volume = {8} } @Article{Keil:2006:CER, Title = {Computational Experience with Rigorous Error Bounds for the Netlib Linear Programming Library}, Author = {C. Keil and C. Jansson}, Journal = {Reliable Computing}, Year = {2006}, Number = {4}, Pages = {303--321}, Volume = {12} } @Article{Keiper:1993:IAM, Title = {Interval Arithmetic in {M}athematica}, Author = {J. B. Keiper}, Journal = {Interval Computations}, Year = {1993}, Number = {3}, Pages = {76--87} } @Article{Kempken:2011:VFM, Title = {Verifed Factorization Methods for {SMP/G/1} Queueing Systems and their Interplay in an Integrated Problem-Solving Environment}, Author = {Sebastian Kempken and Wolfram Luther}, Journal = {Reliable Computing}, Year = {2011}, Month = {Jul}, Number = {3}, Pages = {179--192}, Volume = {15} } @Article{Khlebalin:1992:IAS, Title = {Interval automatic systems --- theory, computer-aided design and application}, Author = {N. A. Khlebalin}, Journal = {Interval Computations}, Year = {1992}, Number = {3}, Pages = {106--115} } @Article{Kieffer:2000:RAR, Title = {Robust Autonomous Robot Localization Using Interval Analysis}, Author = {M. Kieffer and L. Jaulin and E. Walter and D. Meizel}, Journal = {Reliable Computing}, Year = {2000}, Number = {3}, Pages = {337--361}, Volume = {6} } @Article{Kiel:2012:YYA, Title = {{YalAA}: {Y}et Another Library for Affine Arithmetic}, Author = {Stefan Kiel}, Journal = {Reliable Computing}, Year = {2012}, Month = {Sep}, Number = {1}, Pages = {114--129}, Volume = {16} } @Article{Kiel:2014:ETV, Title = {An Environment for Testing, Verification and Validation of Dynamical Models in the Context of Solid Oxide Fuel Cells}, Author = {Stefan Kiel and Ekaterina Auer and Andreas Rauh}, Journal = {Reliable Computing}, Year = {2014}, Month = {May}, Number = {3}, Pages = {302--317}, Volume = {19} } @Article{Kirchner:2006:HSI, Title = {Hardware Support for Interval Arithmetic}, Author = {R. Kirchner and U. W. Kulisch}, Journal = {Reliable Computing}, Year = {2006}, Number = {3}, Pages = {225--227}, Volume = {12} } @Article{Kohout:2004:CIF, Title = {Characterization of Interval Fuzzy Logic Systems of Connectives by Group Transformations}, Author = {L. J. Kohout and E. Kim}, Journal = {Reliable Computing}, Year = {2004}, Number = {4}, Pages = {299--334}, Volume = {10} } @Article{Kohout:1993:IVI, Title = {Interval-Valued Inference in Medical Knowledge-Based System {CLINAID}}, Author = {L. J. Kohout and I. Stabile}, Journal = {Interval Computations}, Year = {1993}, Number = {3}, Pages = {88--115} } @Article{Kohout:1995:IB, Title = {Parallel interval-based reasoning in medical knowledge-based system {CLINAID}}, Author = {L. J. Kohout and I. Stabile and H. Kalantar and M. F. San-Andres and J. Anderson}, Journal = {Reliable Computing}, Year = {1995}, Number = {2}, Pages = {109--140}, Volume = {1} } @Article{Kolberg:2011:EPS, Title = {Efficient Parallel Solvers for Large Dense Systems of Linear Interval Equations}, Author = {Mariana Kolberg and Walter Kr{\"{a}}mer and Michael Zimmer}, Journal = {Reliable Computing}, Year = {2011}, Month = {Jul}, Number = {3}, Pages = {193--206}, Volume = {15} } @Article{Kolev:2016:CIM, Title = {A Class of Iterative Methods for Determining $p$--Solutions of Linear Interval Parametric Systems}, Author = {Lubomir V. Kolev}, Journal = {Reliable Computing}, Year = {2016}, Month = {May}, Number = {1}, Pages = {26--46}, Volume = {22} } @Article{Kolev:2014:CDI, Title = {Componentwise Determination of the Interval Hull Solution for Linear Interval Parameter Systems}, Author = {Lyubomir V. Kolev}, Journal = {Reliable Computing}, Year = {2014}, Month = {Mar}, Number = {1}, Pages = {1--24}, Volume = {20} } @Article{Kolev:2011:MDR, Title = {A Method for Determining the Regularity Radius of Interval Matrices}, Author = {Lubomir V. Kolev}, Journal = {Reliable Computing}, Year = {2011}, Month = {Jul}, Number = {1}, Pages = {1--26}, Volume = {16} } @Article{Kolev:2007:DPD, Title = {Determining the Positive Definiteness Margin of Interval Matrices}, Author = {L. V. Kolev}, Journal = {Reliable Computing}, Year = {2007}, Number = {6}, Pages = {445--466}, Volume = {13} } @Article{Kolev:2007:OMG, Title = {Optimal Multiplication of G-intervals}, Author = {L. V. Kolev}, Journal = {Reliable Computing}, Year = {2007}, Number = {5}, Pages = {399--408}, Volume = {13} } @Article{Kolev:2006:IDM, Title = {Improvement of a Direct Method for Outer Solution of Linear Parametric Systems}, Author = {L. V. Kolev}, Journal = {Reliable Computing}, Year = {2006}, Number = {3}, Pages = {193--202}, Volume = {12} } @Article{Kolev:2006:NFM, Title = {New Formulae for Multiplication of Intervals}, Author = {L. V. Kolev}, Journal = {Reliable Computing}, Year = {2006}, Number = {4}, Pages = {281--292}, Volume = {12} } @Article{Kolev:2006:OIS, Title = {Outer Interval Solution of the Eigenvalue Problem under General Form Parametric Dependencies}, Author = {L. V. Kolev}, Journal = {Reliable Computing}, Year = {2006}, Number = {2}, Pages = {121--140}, Volume = {11} } @Article{Kolev:2004:MOI, Title = {A Method for Outer Interval Solution of Linear Parametric Systems}, Author = {L. V. Kolev}, Journal = {Reliable Computing}, Year = {2004}, Number = {3}, Pages = {227--239}, Volume = {10} } @Article{Kolev:2002:OSL, Title = {Outer Solution of Linear Systems Whose Elements Are Affine Functions of Interval Parameters}, Author = {L. V. Kolev}, Journal = {Reliable Computing}, Year = {2002}, Number = {6}, Pages = {493--501}, Volume = {8} } @Article{Kolev:2001:ACL, Title = {Automatic Computation of a Linear Interval Enclosure}, Author = {L. V. Kolev}, Journal = {Reliable Computing}, Year = {2001}, Number = {1}, Pages = {17--28}, Volume = {7} } @Article{Kolev:1999:IMG, Title = {An Improved Method for Global Solution of Non-Linear Systems}, Author = {L. V. Kolev}, Journal = {Reliable Computing}, Year = {1999}, Number = {2}, Pages = {103--111}, Volume = {5} } @Article{Kolev:1998:NMG, Title = {A New Method for Global Solution of Systems of Non-Linear Equations}, Author = {L. V. Kolev}, Journal = {Reliable Computing}, Year = {1998}, Number = {2}, Pages = {125--146}, Volume = {4} } @Article{Kolev:1993:UIS, Title = {Use of Interval Slopes for the Irrational Part of Factorable Functions}, Author = {L. V. Kolev}, Journal = {Interval Computations}, Year = {1993}, Number = {1}, Pages = {83--93}, Volume = {3} } @Article{Kolev:2001:CTB, Title = {Cheap and Tight Bounds on the Solution Set of Perturbed Systems of Nonlinear Equations}, Author = {L. V. Kolev and I. P. Nenov}, Journal = {Reliable Computing}, Year = {2001}, Number = {5}, Pages = {399--408}, Volume = {7} } @Article{Korlyukov:1992:NAI, Title = {A new application of interval mathematics}, Author = {A. V. Korlyukov}, Journal = {Interval Computations}, Year = {1992}, Number = {3}, Pages = {116--121} } @Article{Korn:1993:VSL, Title = {Verified Solution of Linear Systems Based on Common Software Libraries}, Author = {C. F. Korn and Ch. Ullrich}, Journal = {Interval Computations}, Year = {1993}, Number = {3}, Pages = {116--132} } @Article{Koshelev:2000:ESF, Title = {Every Superinterval of the Function Range Can Be an Interval-Computations Enclosure}, Author = {M. Koshelev}, Journal = {Reliable Computing}, Year = {2000}, Number = {2}, Pages = {219--223}, Volume = {6} } @Article{Koshelev:1998:BDG, Title = {A Brief Description of {G}ell-{M}ann's Lecture and How Intervals May Help to Describe Complexity in the Real World}, Author = {M. Koshelev and L. Longpre}, Journal = {Reliable Computing}, Year = {1998}, Number = {1}, Pages = {105--107}, Volume = {4} } @Article{Koshelev:1998:OEQ, Title = {Optimal Enclosure of Quadratic Interval Functions}, Author = {M. Koshelev and L. Longpre and P. Taillibert}, Journal = {Reliable Computing}, Year = {1998}, Number = {4}, Pages = {351--360}, Volume = {4} } @Article{Kosheleva:1999:IES, Title = {Interval Estimates for Signal Processing: Special Purpose Hardware}, Author = {O. Kosheleva and S. D. Cabrera and G. A. Gibson and S. Cherukuri}, Journal = {Reliable Computing}, Year = {1999}, Number = {2}, Pages = {175--196}, Volume = {5} } @Article{Kosheleva:1999:EEI, Title = {Error Estimation for Indirect Measurements: Interval Computation Problem Is (Slightly) Harder Than a Similar Probabilistic Computational Problem}, Author = {O. Kosheleva and V. Kreinovich}, Journal = {Reliable Computing}, Year = {1999}, Number = {1}, Pages = {81--95}, Volume = {5} } @Article{Kosheleva:1999:OIP, Title = {Only Intervals Preserve the Invertibility of Arithmetic Operations}, Author = {O. Kosheleva and V. Kreinovich}, Journal = {Reliable Computing}, Year = {1999}, Number = {4}, Pages = {385--394}, Volume = {5} } @Article{Kosheleva:1998:WPI, Title = {When Is the Product of Intervals Also an Interval?}, Author = {O. Kosheleva and P. G. Vroegindeweij}, Journal = {Reliable Computing}, Year = {1998}, Number = {2}, Pages = {179--190}, Volume = {4} } @Article{Kosheleva:1998:HPA, Title = {Hilbert Problems (Almost) 100 Years Later (From the Viewpoint of Interval Computations)}, Author = {O. M. Kosheleva}, Journal = {Reliable Computing}, Year = {1998}, Number = {4}, Pages = {399--403}, Volume = {4} } @Article{Kostousova:2013:BUP, Title = {On Boundedness and Unboundedness of Polyhedral Estimates for Reachable Sets of Linear Differential Systems}, Author = {Elena K. Kostousova}, Journal = {Reliable Computing}, Year = {2013}, Month = {Nov}, Number = {1}, Pages = {26--44}, Volume = {19} } @Article{Kozina:2004:DOP, Title = {Discrete Optimization Problems with Interval Data: {P}areto Set of Solutions or Set of Weak Solutions?}, Author = {G. L. Kozina}, Journal = {Reliable Computing}, Year = {2004}, Number = {6}, Pages = {469--487}, Volume = {10} } @Article{Kozina:1994:IST, Title = {Interval Spanning Trees Problem: Solvability and Computational Complexity}, Author = {G. L. Kozina and V. A. Perepelitsa}, Journal = {Interval Computations}, Year = {1994}, Number = {1}, Pages = {42--50} } @Article{Kozine:2002:IVF, Title = {Interval-Valued Finite {M}arkov Chains}, Author = {I. O. Kozine and L. V. Utkin}, Journal = {Reliable Computing}, Year = {2002}, Number = {2}, Pages = {97--113}, Volume = {8} } @Article{Kraemer:1996:AFE, Title = {Automatic Forward Error Analysis for Floating Point Algorithms}, Author = {W. Kraemer and A. Bantle}, Journal = {Reliable Computing}, Year = {2001}, Number = {4}, Pages = {321--340}, Volume = {7} } @Article{Kraemer:2003:EIP, Title = {Extended Interval Power Function}, Author = {W. Kraemer and J. Wolff von Gudenberg}, Journal = {Reliable Computing}, Year = {2003}, Number = {5}, Pages = {339--347}, Volume = {9} } @Article{Kraemer:1996:TAG, Title = {Two adaptive {G}auss-{L}egendre type algorithms for the verified computation of definite integrals}, Author = {W. Kraemer and S. Wedner}, Journal = {Reliable Computing}, Year = {1996}, Number = {3}, Pages = {241--254}, Volume = {2} } @Article{Kreinovich:2016:SSG, Title = {Standing on the Shoulders of the Giants: {W}hy Constructive Mathematics, Probability Theory, Interval Mathematics, and Fuzzy Mathematics Are Important}, Author = {Vladik Kreinovich}, Journal = {Reliable Computing}, Year = {2016}, Month = {Jul}, Number = {1}, Pages = {97--104}, Volume = {23} } @Article{Kreinovich:2005:OFC, Title = {Optimal Finite Characterization of Linear Problems with Inexact Data}, Author = {V. Kreinovich}, Journal = {Reliable Computing}, Year = {2005}, Number = {6}, Pages = {479--489}, Volume = {11} } @Article{Kreinovich:2002:REN, Title = {Range Estimation Is {NP}-Hard for {$\varepsilon^2$} Accuracy and Feasible for {$\varepsilon^{2-d}$}}, Author = {V. Kreinovich}, Journal = {Reliable Computing}, Year = {2002}, Number = {6}, Pages = {481--491}, Volume = {8} } @Article{Kreinovich:2001:RFN, Title = {Roundoff-Free Number Fields for Interval Computations}, Author = {V. Kreinovich}, Journal = {Reliable Computing}, Year = {2001}, Number = {1}, Pages = {41--47}, Volume = {7} } @Article{Kreinovich:1996:MEI, Title = {Maximum entropy and interval computations ({S}eptember notes on summer impressions)}, Author = {V. Kreinovich}, Journal = {Reliable Computing}, Year = {1996}, Number = {1}, Pages = {63--80}, Volume = {2} } @Article{Kreinovich:1995:WIS, Title = {Why intervals? {A} simple limit theorem that is similar to limit theorems from statistics}, Author = {V. Kreinovich}, Journal = {Reliable Computing}, Year = {1995}, Number = {1}, Pages = {33--40}, Volume = {1} } @Article{Kreinovich:2007:MCT, Title = {Monte-Carlo-Type Techniques for Processing Interval Uncertainty, and Their Potential Engineering Applications}, Author = {V. Kreinovich and J. Beck and C. Ferregut and A. Sanchez and G. R. Keller and M. Averill and S. A. Starks}, Journal = {Reliable Computing}, Year = {2007}, Number = {1}, Pages = {25--69}, Volume = {13} } @Article{Kreinovich:1997:SSS, Title = {Is Solar System Stable? A Remark}, Author = {V. Kreinovich and A. Bernat}, Journal = {Reliable Computing}, Year = {1997}, Number = {2}, Pages = {149--154}, Volume = {3} } @Article{Kreinovich:1994:PAI, Title = {Parallel Algorithms for Interval Computations: An Introduction}, Author = {V. Kreinovich and A. Bernat}, Journal = {Interval Computations}, Year = {1994}, Number = {3}, Pages = {6--62} } @Article{Kreinovich:1992:IEC, Title = {Interval estimates for closure-phase and closure-amplitude in radio astronomy}, Author = {V. Kreinovich and A. Bernat and O. Kosheleva and A. Finkelstein}, Journal = {Interval Computations}, Year = {1992}, Number = {2}, Pages = {51--71} } @Article{Kreinovich:1991:PCE, Title = {Parallel Computers Estimate errors caused by imprecise data}, Author = {V. Kreinovich and A. Bernat and E. Villa and Y. Mariscal}, Journal = {Interval Computations}, Year = {1991}, Number = {2}, Pages = {31--46} } @Article{Kreinovich:2003:EUB, Title = {Exact Upper Bound on the Mean of the Product of Many Random Variables with Known Expectations}, Author = {V. Kreinovich and S. Ferson and L. Ginzburg}, Journal = {Reliable Computing}, Year = {2003}, Number = {6}, Pages = {441--463}, Volume = {9} } @Article{Kreinovich:1996:LIE, Title = {Linear interval equations: Computing enclosures with bounded relative or absolute overestimation is NP-hard}, Author = {V. Kreinovich and A. V. Lakeyev}, Journal = {Reliable Computing}, Year = {1996}, Number = {4}, Pages = {341--350}, Volume = {2} } @Article{Kreinovich:1993:OSI, Title = {Optimal solution of interval linear systems is intractable ({NP}-hard)}, Author = {V. Kreinovich and A. V. Lakeyev and S. I. Noskov}, Journal = {Interval Computations}, Year = {1993}, Number = {1}, Pages = {6--14} } @Article{Kreinovich:2003:ECN, Title = {Are There Easy-to-Check Necessary and Sufficient Conditions for Straightforward Interval Computations To Be Exact?}, Author = {V. Kreinovich and L. Longpre and J. J. Buckley}, Journal = {Reliable Computing}, Year = {2003}, Number = {5}, Pages = {349--358}, Volume = {9} } @Article{Kreinovich:2005:ODI, Title = {Outlier Detection under Interval Uncertainty: Algorithmic Solvability and Computational Complexity}, Author = {V. Kreinovich and L. Longpre and P. Patangay and S. Ferson and L. Ginzburg}, Journal = {Reliable Computing}, Year = {2005}, Number = {1}, Pages = {59--76}, Volume = {11} } @Article{Kreinovich:2007:IRT, Title = {Interval-Related Talks at the International Conference on Finite Element Methods in Engineering and Science}, Author = {V. Kreinovich and R. Muhanna}, Journal = {Reliable Computing}, Year = {2007}, Number = {4}, Pages = {375--379}, Volume = {13} } @Article{Kreinovich:1995:AIC, Title = {Applications of interval computations to earthquake-resistant engineering: {H}ow to compute derivatives of interval functions fast}, Author = {V. Kreinovich and D. Nemir and E. Gutierrez}, Journal = {Reliable Computing}, Year = {1995}, Number = {2}, Pages = {141--172}, Volume = {1} } @Article{Kreinovich:1996:IMG, Title = {Interval methods that are guaranteed to underestimate (and the resulting new justification of {K}aucher arithmetic)}, Author = {V. Kreinovich and V. M. Nesterov and N. A. Zheludeva}, Journal = {Reliable Computing}, Year = {1996}, Number = {2}, Pages = {119--124}, Volume = {2} } @Article{Kreinovich:1995:ISN, Title = {Interval sessions at {NAFIPS/IFIS/NASA'94}}, Author = {V. Kreinovich and H. T. Nguyen}, Journal = {Reliable Computing}, Year = {1995}, Number = {1}, Pages = {93--98}, Volume = {1} } @Article{Kreinovich:2006:OUM, Title = {Towards Optimal Use of Multi-Precision Arithmetic: A Remark}, Author = {V. Kreinovich and S. Rump}, Journal = {Reliable Computing}, Year = {2006}, Number = {5}, Pages = {365--369}, Volume = {12} } @Article{Kreinovich:2016:IMD, Title = {Interval Methods for Data Fitting under Uncertainty: {A} Probabilistic Treatment}, Author = {Vladik Kreinovich and Sergey P. Shary}, Journal = {Reliable Computing}, Year = {2016}, Month = {Jul}, Number = {1}, Pages = {105--140}, Volume = {23} } @Article{Kreinovich:1997:TJC, Title = {On a Theoretical Justification of the Choice of Epsilon-Inflation in {PASCAL-XSC}}, Author = {V. Kreinovich and S. Starks and G. Mayer}, Journal = {Reliable Computing}, Year = {1997}, Number = {4}, Pages = {437--445}, Volume = {3} } @Article{Kreinovich:1994:IAT, Title = {Interval Approach to Testing Software}, Author = {V. Kreinovich and T. Swenson and A. Elentukh}, Journal = {Interval Computations}, Year = {1994}, Number = {2}, Pages = {90--109} } @Article{Kreinovich:1996:QTA, Title = {A quadratic-time algorithm for smoothing interval functions}, Author = {V. Kreinovich and K. Villaverde}, Journal = {Reliable Computing}, Year = {1996}, Number = {3}, Pages = {255--264}, Volume = {2} } @Article{Kreinovich:2006:CPI, Title = {Towards Combining Probabilistic and Interval Uncertainty in Engineering Calculations: Algorithms for Computing Statistics under Interval Uncertainty, and Their Computational Complexity}, Author = {V. Kreinovich and G. Xiang and S. A. Starks and L. Longpre and M. Ceberio and R. Araiza and J. Beck and R. Kandathi and A. Nayak and R. Torres and J. G. Hajagos}, Journal = {Reliable Computing}, Year = {2006}, Number = {6}, Pages = {471--501}, Volume = {12} } @Article{Krishchuk:1992:IOF, Title = {Interval operations and functions library for {FORTRAN} 77 programming system and its practice using}, Author = {V. N. Krishchuk and N. M. Vasilega and G. L. Kozina}, Journal = {Interval Computations}, Year = {1992}, Number = {4}, Pages = {2--8} } @Article{Kristinsdottir:1993:MTI, Title = {Methodologies for Tolerance Intervals}, Author = {B. P. Kristinsdottir and Z. B. Zabinsky and T. Csendes and M. E. Tuttle}, Journal = {Interval Computations}, Year = {1993}, Number = {3}, Pages = {133--147} } @Article{Krymsky:1992:AIR, Title = {Algorithmic aims of reliability provision for large-scale dynamic systems with interval parameters}, Author = {V. G. Krymsky}, Journal = {Interval Computations}, Year = {1992}, Number = {4}, Pages = {9--13} } @Article{Kubica:2014:ERU, Title = {Excluding Regions Using Sobol Sequences in an Interval Branch--and--Prune Method for Nonlinear Systems}, Author = {Bart{\l{}}omiej Jacek Kubica}, Journal = {Reliable Computing}, Year = {2014}, Month = {Jun}, Number = {4}, Pages = {385--397}, Volume = {19} } @Article{Kubica:2011:IMS, Title = {Interval Methods for Solving Underdetermined Nonlinear Systems}, Author = {Bart{\l{}}omiej Jacek Kubica}, Journal = {Reliable Computing}, Year = {2011}, Month = {Jul}, Number = {3}, Pages = {207--217}, Volume = {15} } @Article{Kubica:2005:IGO, Title = {An Interval Global Optimization Algorithm Combining Symbolic Rewriting and Componentwise Newton Method Applied to Control a Class of Queueing Systems}, Author = {B. J. Kubica and K. Malinowski}, Journal = {Reliable Computing}, Year = {2005}, Number = {5}, Pages = {393--411}, Volume = {11} } @Article{Kulisch:2016:HSA, Title = {High Speed Associative Accumulation of Floating--point Numbers and Floating--point Intervals}, Author = {Ulrich Kulisch and Gerd Bohlender}, Journal = {Reliable Computing}, Year = {2016}, Month = {Jul}, Number = {1}, Pages = {141--153}, Volume = {23} } @Article{Kulpa:2003:DAI1, Title = {Diagrammatic Analysis of Interval Linear Equations: Part I: Basic Notions and the One-Dimensional Case}, Author = {Z. Kulpa}, Journal = {Reliable Computing}, Year = {2003}, Number = {1}, Pages = {1--20}, Volume = {9} } @Article{Kulpa:2003:DAI2, Title = {Diagrammatic Analysis of Interval Linear Equations. Part II: The Two-Dimensional Case and Generalization to n Dimensions}, Author = {Z. Kulpa}, Journal = {Reliable Computing}, Year = {2003}, Number = {3}, Pages = {205--228}, Volume = {9} } @Article{Kulpa:1997:DRI, Title = {Diagrammatic Representation of Interval Space in Proving Theorems about Interval Relations }, Author = {Z. Kulpa}, Journal = {Reliable Computing}, Year = {1997}, Number = {3}, Pages = {209--217}, Volume = {3} } @Article{Kumkov:2016:EPC, Title = {An Estimation Problem of Chemical Process with Confluent Parameters: {A}n Interval Approach}, Author = {Sergey I. Kumkov}, Journal = {Reliable Computing}, Year = {2016}, Month = {Mar}, Number = {1}, Pages = {15--25}, Volume = {22} } @Article{Kumkov:2013:IAT, Title = {Interval Approach to Identification of Catalytic Process Parameters}, Author = {Sergey I. Kumkov and Yuliya V. Mikushina}, Journal = {Reliable Computing}, Year = {2013}, Month = {Nov}, Number = {2}, Pages = {197--214}, Volume = {19} } @Article{Kupriyanova:1995:IEU, Title = {Inner estimation of the united solution set of interval linear algebraic system}, Author = {L. Kupriyanova}, Journal = {Reliable Computing}, Year = {1995}, Number = {1}, Pages = {15--32}, Volume = {1} } @Article{Labutin:2013:ASA, Title = {Algorithm for Sparse Approximate Inverse Preconditioners in the Conjugate Gradient Method}, Author = {Ilya B. Labutin and Irina V. Surodina}, Journal = {Reliable Computing}, Year = {2013}, Month = {Dec}, Number = {1}, Pages = {120--126}, Volume = {19} } @Article{Lagrange:2007:SCI, Title = {On Sufficient Conditions of the Injectivity: Development of a Numerical Test Algorithm via Interval Analysis}, Author = {S. Lagrange and N. Delanoue and L. Jaulin}, Journal = {Reliable Computing}, Year = {2007}, Number = {5}, Pages = {409--421}, Volume = {13} } @Article{Lakeyev:2014:UGS, Title = {On Unboundedness of Generalized Solution Sets for Interval Linear Systems}, Author = {Anatoly V. Lakeyev}, Journal = {Reliable Computing}, Year = {2014}, Month = {Apr}, Number = {3}, Pages = {290--301}, Volume = {19} } @Article{Lakeyev:1996:CCS, Title = {On the computational complexity of the solution of linear systems with moduli}, Author = {A. V. Lakeyev}, Journal = {Reliable Computing}, Year = {1996}, Number = {2}, Pages = {125--132}, Volume = {2} } @Article{Lakeyev:1996:NHC, Title = {{NP}-Hard Classes of Linear Algebraic Systems with Uncertainties}, Author = {A. V. Lakeyev and V. Kreinovich}, Journal = {Reliable Computing}, Year = {1996}, Number = {1}, Pages = {51--81}, Volume = {3} } @Article{Laranjeira:2016:BUM, Title = {Building Underwater Mosaics Using Navigation Data and Feature Extraction}, Author = {M. Laranjeira and Luc Jaulin and S. Tauvry}, Journal = {Reliable Computing}, Year = {2016}, Month = {Aug}, Number = {1}, Pages = {116--137}, Volume = {22} } @Article{Lea:1996:OIE, Title = {Optimal interval enclosures for fractionally-linear functions, and their application to intelligent control}, Author = {R. N. Lea and V. Kreinovich and R. Trejo}, Journal = {Reliable Computing}, Year = {1996}, Number = {3}, Pages = {265--286}, Volume = {2} } @Article{Leclerc:1993:PIG, Title = {Parallel Interval Global Optimization and Its Implementation in {C}++}, Author = {A. Leclerc}, Journal = {Interval Computations}, Year = {1993}, Number = {3}, Pages = {148--163} } @Article{Leclerc:1998:RCD, Title = {Reliable Collision Detection for Time-Dependent Parametric Surfaces}, Author = {A. Leclerc and J. Ely}, Journal = {Reliable Computing}, Year = {1998}, Number = {4}, Pages = {331--344}, Volume = {4} } @Article{Lerch:1999:ETD, Title = {Expression Templates for Dot Product Expressions}, Author = {M. Lerch and J. Wolff von Gudenberg}, Journal = {Reliable Computing}, Year = {1999}, Number = {1}, Pages = {69--80}, Volume = {5} } @Article{Leroy:2012:CUS, Title = {Convergence under Subdivision and Complexity of Polynomial Minimization in the Simplicial {B}ernstein Basis}, Author = {Richard Leroy}, Journal = {Reliable Computing}, Year = {2012}, Month = {Dec}, Number = {1}, Pages = {11--21}, Volume = {17} } @Article{Levichev:1998:IST, Title = {Intervals in Space-Time: {A. D. A}lexandrov is 85}, Author = {A. Levichev and O. Kosheleva}, Journal = {Reliable Computing}, Year = {1998}, Number = {1}, Pages = {109--112}, Volume = {4} } @Article{Lin:2006:RMO, Title = {Reliable Modeling and Optimization for Chemical Engineering Applications: Interval Analysis Approach}, Author = {Y. Lin and C. R. Gwaltney and M. A. Stadtherr}, Journal = {Reliable Computing}, Year = {2006}, Number = {6}, Pages = {427--450}, Volume = {12} } @Article{Litvinov:1992:EAI, Title = {Error auto-correction in rational approximation}, Author = {G. L. Litvinov}, Journal = {Interval Computations}, Year = {1992}, Number = {4}, Pages = {14--18} } @Article{Litvinov:2001:IIA, Title = {Idempotent Interval Analysis and Optimization Problems}, Author = {G. L. Litvinov and A. N. Sobolevskii}, Journal = {Reliable Computing}, Year = {2001}, Number = {5}, Pages = {353--377}, Volume = {7} } @Article{Lodwick:2003:EVC, Title = {Estimating and Validating the Cumulative Distribution of a Function of Random Variables: Toward the Development of Distribution Arithmetic}, Author = {W. A. Lodwick and K. D. Jamison}, Journal = {Reliable Computing}, Year = {2003}, Number = {2}, Pages = {127--141}, Volume = {9} } @Article{Loh:2002:RER, Title = {(R)ump's Example Revisited}, Author = {E. Loh and G. W. Walster}, Journal = {Reliable Computing}, Year = {2002}, Number = {3}, Pages = {245--248}, Volume = {8} } @Article{Longpre:1997:ICW, Title = {Interval and Complexity Workshops Back-to-Back with 1997 {ACM} {S}ymposium on {T}heory of {C}omputing ({STOC'97})}, Author = {L. Longpre and M. Berz}, Journal = {Reliable Computing}, Year = {1997}, Number = {4}, Pages = {453--457}, Volume = {3} } @Article{Lordelo:2006:ADR, Title = {Analysis and Design of Robust Controllers Using the Interval Diophantine Equation}, Author = {A. D. S. Lordelo and E. A. Juzzo and P. A. V. Ferreira}, Journal = {Reliable Computing}, Year = {2006}, Number = {5}, Pages = {371--388}, Volume = {12} } @Article{Lorkowski:2015:WCW, Title = {When Can We Reduce Multi--Variable Range Estimation Problems to Two Fewer--Variable Problems?}, Author = {Joe Lorkowski and Olga Kosheleva and Luc Longpr{\'e} and Vladik Kreinovich}, Journal = {Reliable Computing}, Year = {2015}, Month = {Aug}, Number = {1}, Pages = {1--10}, Volume = {21} } @Article{Lorkowski:1996:MNG, Title = {If we measure a number, we get an interval. What if we measure a function or an operator?}, Author = {J. Lorkowski and V. Kreinovich}, Journal = {Reliable Computing}, Year = {1996}, Number = {3}, Pages = {287--298}, Volume = {2} } @Article{Luther:1994:CSI, Title = {Computation of Standard Interval Functions in Multiple-Precision Interval Arithmetic}, Author = {W. Luther and W. Otten}, Journal = {Interval Computations}, Year = {1994}, Number = {4}, Pages = {78--99} } @Article{Luther:1994:VIE, Title = {Verified Inclusion for Eigenvalues of {H}ill's Equation}, Author = {W. J. Luther and W. Otten}, Journal = {Interval Computations}, Year = {1994}, Number = {1}, Pages = {28--41} } @Article{Lyager:1994:FLE, Title = {Finding Local Extremal Points by Using Parallel Interval Methods}, Author = {E. Lyager}, Journal = {Interval Computations}, Year = {1994}, Number = {3}, Pages = {63--80} } @Article{Lyashko:2005:OSI, Title = {The Optimal Solution of an Interval System of Linear Algebraic Equations}, Author = {M. A. Lyashko}, Journal = {Reliable Computing}, Year = {2005}, Number = {2}, Pages = {105--127}, Volume = {11} } @Article{Lyashko:1996:SCT, Title = {On the speed of convergence of the total step iterative method for a class of interval linear algebraic systems}, Author = {M. A. Lyashko}, Journal = {Reliable Computing}, Year = {1996}, Number = {4}, Pages = {351--356}, Volume = {2} } @Article{Lynch:1996:SHR, Title = {Software for high radix on-line arithmetic}, Author = {T. Lynch and M. J. Schulte}, Journal = {Reliable Computing}, Year = {1996}, Number = {2}, Pages = {133--138}, Volume = {2} } @Article{Lyudvin:2013:TIP, Title = {Testing Implementations of {PPS}--methods for Interval Linear Systems}, Author = {Dmitri Yu. Lyudvin and Sergey P. Shary}, Journal = {Reliable Computing}, Year = {2013}, Month = {Dec}, Number = {2}, Pages = {176--196}, Volume = {19} } @Article{Madsen:1994:PML, Title = {A Parallel Method for Linear Interval Equations}, Author = {K. Madsen and O. Toft}, Journal = {Interval Computations}, Year = {1994}, Number = {3}, Pages = {81--105} } @Article{Magoc:2011:UPC, Title = {Using Preference Constraints to Solve Multi-Criteria Decision Making Problems}, Author = {Tanja Mago{\v{c}} and Martine Ceberio and Francois Modave}, Journal = {Reliable Computing}, Year = {2011}, Month = {Jul}, Number = {3}, Pages = {218--229}, Volume = {15} } @Article{Magoc:2011:AFM, Title = {Applications of Fuzzy Measures and Intervals in Finance}, Author = {Tanja Mago{\v{c}} and Xiaojing Wang and Francois Modave and Martine Ceberio}, Journal = {Reliable Computing}, Year = {2011}, Month = {Jul}, Number = {4}, Pages = {300--311}, Volume = {15} } @Article{Makino:1994:ECD, Title = {Efficient Control of the Dependency Problem Based on Taylor Model Methods}, Author = {K. Makino and M. Berz}, Journal = {Reliable Computing}, Year = {1999}, Number = {1}, Pages = {3--12}, Volume = {5} } @Article{Markov:2016:AOI, Title = {On the Algebra of Intervals}, Author = {Svetoslav Markov}, Journal = {Reliable Computing}, Year = {2016}, Month = {Jun}, Number = {1}, Pages = {80--108}, Volume = {21} } @Article{Markov:2001:API, Title = {On the Algebraic Properties of Intervals and Some Applications}, Author = {S. Markov}, Journal = {Reliable Computing}, Year = {2001}, Number = {2}, Pages = {113--127}, Volume = {7} } @Article{Markov:2001:MI, Title = {The Mystery of Intervals}, Author = {S. Markov}, Journal = {Reliable Computing}, Year = {2001}, Number = {1}, Pages = {63--65}, Volume = {7} } @Article{Markov:1997:IEA, Title = {Isomorphic Embeddings of Abstract Interval Systems}, Author = {S. M. Markov}, Journal = {Reliable Computing}, Year = {1997}, Number = {3}, Pages = {199--207}, Volume = {3} } @Article{Markov:1993:SIP, Title = {Some Interpolation Problems Involving Interval Data}, Author = {S. M. Markov}, Journal = {Interval Computations}, Year = {1993}, Number = {3}, Pages = {164--182} } @Article{Markov:1992:PRM, Title = {On the presentation of ranges of monotone functions using interval arithmetic}, Author = {S. M. Markov}, Journal = {Interval Computations}, Year = {1992}, Number = {4}, Pages = {19--31} } @Article{Mayer:2006:CFI, Title = {A Contribution to the Feasibility of the Interval Gaussian Algorithm}, Author = {G. Mayer}, Journal = {Reliable Computing}, Year = {2006}, Number = {2}, Pages = {79--98}, Volume = {11} } @Article{Mayer:1998:AIG, Title = {On the Applicability of the Interval Gaussian Algorithm}, Author = {G. Mayer and J. Rohn}, Journal = {Reliable Computing}, Year = {1998}, Number = {3}, Pages = {205--222}, Volume = {4} } @Article{Mayer:2012:EMR, Title = {On an Expression for the Midpoint and the Radius of the Product of Two Intervals}, Author = {G{\"{u}}nter Mayer}, Journal = {Reliable Computing}, Year = {2012}, Month = {Oct}, Number = {1}, Pages = {210--224}, Volume = {16} } @Article{Mayer:2002:AOD, Title = {An Approach to Overcome Division by Zero in the Interval Gauss Algorithm}, Author = {J. Mayer}, Journal = {Reliable Computing}, Year = {2002}, Number = {3}, Pages = {229--237}, Volume = {8} } @Article{McLean:1995:SST, Title = {Study on sampling techniques with {CMM}s}, Author = {T. J. McLean and D. H. Xu}, Journal = {Reliable Computing}, Year = {1995}, Number = {3}, Pages = {275--284}, Volume = {1} } @Article{Meer:2004:RAS, Title = {On a Refined Analysis of Some Problems in Interval Arithmetic Using Real Number Complexity Theory}, Author = {K. Meer}, Journal = {Reliable Computing}, Year = {2004}, Number = {3}, Pages = {209--225}, Volume = {10} } @Article{Menshikov:2001:PEO, Title = {The Preliminary Enclosing of the {ODE} Solutions on the Base of the {C}auchy-{D}uhamel Identity}, Author = {G. G. Menshikov}, Journal = {Reliable Computing}, Year = {2001}, Number = {6}, Pages = {485--495}, Volume = {7} } @Article{Menshikov:1998:ISI, Title = {Intersection Subdistributivity and Interval Hull Superdistributivity with Respect to the Interval Maps}, Author = {G. G. Menshikov}, Journal = {Reliable Computing}, Year = {1998}, Number = {4}, Pages = {377--381}, Volume = {4} } @Article{Menshikov:1994:DDI, Title = {On Different Definitions of Interval Extension: Problems of Teaching}, Author = {G. G. Menshikov}, Journal = {Interval Computations}, Year = {1994}, Number = {1}, Pages = {96--98} } @Article{Menshikov:1992:ICD, Title = {Interval co-integration of differential equations connected by a substitution of the variable}, Author = {G. G. Menshikov}, Journal = {Interval Computations}, Year = {1992}, Number = {4}, Pages = {32--36} } @Article{Menshikov:1992:TEI, Title = {The teaching experience of interval computations at the Department of applied mathematics and control processes of {S}t. {P}etersburg University}, Author = {G. G. Menshikov}, Journal = {Interval Computations}, Year = {1992}, Number = {2}, Pages = {83--85} } @Article{Menshikov:2001:SSR, Title = {On /\-Subdistributivity and \/-Superdistributivity with Respect to Interval Map in {K}aucher Arithmetic}, Author = {G. G. Menshikov and A. V. Tomashevsky}, Journal = {Reliable Computing}, Year = {2001}, Number = {1}, Pages = {53--57}, Volume = {7} } @Article{Merenyi:1998:HSS, Title = {Hyper-Spectral Satellite Images: Interval Methods May Be Helpful}, Author = {E. Merenyi and S. Starks and K. Villaverde}, Journal = {Reliable Computing}, Year = {1998}, Number = {4}, Pages = {395--397}, Volume = {4} } @Article{Meslem:2010:GPS, Title = {Guaranteed Parameter Set Estimation for Monotone Dynamical Systems Using Hybrid Automata}, Author = {Nacim Meslem and Nacim Ramdani and Yves Candau}, Journal = {Reliable Computing}, Year = {2010}, Month = {Jun}, Number = {1}, Pages = {88--104}, Volume = {14} } @Article{Messine:2006:GRQ, Title = {A General Reliable Quadratic Form: An Extension of Affine Arithmetic}, Author = {F. Messine and A. Touhami}, Journal = {Reliable Computing}, Year = {2006}, Number = {3}, Pages = {171--192}, Volume = {12} } @Article{Michalak:2013:IIP, Title = {Is it Possible to Have a Feasible Enclosure--Computing Method Which Is Independent of the Equivalent Form?}, Author = {Marcin Michalak and Vladik Kreinovich}, Journal = {Reliable Computing}, Year = {2013}, Month = {Jan}, Number = {1}, Pages = {1--8}, Volume = {18} } @Article{Michelucci:2012:CBC, Title = {On the Complexity of the {B}ernstein Combinatorial Problem}, Author = {Dominique Michelucci and Sebti Foufou and Arnaud Kubicki}, Journal = {Reliable Computing}, Year = {2012}, Month = {Dec}, Number = {1}, Pages = {22-- 33}, Volume = {17} } @Article{Milosevic:2012:OMI, Title = {Ostrowski--Like Method for the Inclusion of a Single Complex Polynomial Zero}, Author = {Mimica R. Milo\v{s}evi{\'{c}} and Miodrag S. Petkovi{\'{c}}}, Journal = {Reliable Computing}, Year = {2012}, Month = {Oct}, Number = {1}, Pages = {225--238}, Volume = {16} } @Article{Min:1999:CKM, Title = {On the Componentwise {K}rawczyk-{M}oore Iteration}, Author = {K. Min and L. Qi and S. Zuhe}, Journal = {Reliable Computing}, Year = {1999}, Number = {4}, Pages = {359--370}, Volume = {5} } @Article{Minamihata:2013:FVS, Title = {Fast Verified Solutions of Sparse Linear Systems with {H}--matrices}, Author = {A. Minamihata and K. Sekine and T. Ogita and S. Oishi}, Journal = {Reliable Computing}, Year = {2013}, Month = {Dec}, Number = {2}, Pages = {127--141}, Volume = {19} } @Article{Minamoto:1997:NVS, Title = {Numerical Verifications of Solutions for Nonlinear Parabolic Equations in One-Space Dimensional Case}, Author = {T. Minamoto and M. T. Nakao}, Journal = {Reliable Computing}, Year = {1997}, Number = {2}, Pages = {137--147}, Volume = {3} } @Article{Misane:1995:NCS, Title = {A new characterization of the set of all intervals, based on the necessity to check consistency easily}, Author = {D. Misane and V. Kreinovich}, Journal = {Reliable Computing}, Year = {1995}, Number = {3}, Pages = {285--298}, Volume = {1} } @Article{Miyajima:2015:FES, Title = {Fast Enclosure for Solutions of Generalized Least Squares Problems}, Author = {Shinya Miyajima}, Journal = {Reliable Computing}, Year = {2015}, Month = {Feb}, Number = {1}, Pages = {89--112}, Volume = {20} } @Article{Miyajima:2013:FEM, Title = {Fast Enclosure of Matrix Polynomials}, Author = {Shinya Miyajima}, Journal = {Reliable Computing}, Year = {2013}, Month = {Jan}, Number = {1}, Pages = {9--14}, Volume = {18} } @Article{Miyajima:2012:CEE, Title = {Componentwise Error Estimates for Solutions Obtained by Stationary Iterative Methods}, Author = {Shinya Miyajima}, Journal = {Reliable Computing}, Year = {2012}, Month = {Apr}, Number = {1}, Pages = {102--106}, Volume = {16} } @Article{Miyajima:2012:RBT, Title = {The Relation between Two Types of Error Bounds for Computed Matrix Eigenvalues}, Author = {Shinya Miyajima}, Journal = {Reliable Computing}, Year = {2012}, Month = {Apr}, Number = {1}, Pages = {107--113}, Volume = {16} } @Article{Miyajima:2010:FVA, Title = {Fast Verification for All Eigenpairs in Symmetric Positive Definite Generalized Eigenvalue Problems}, Author = {Shinya Miyajima and Takeshi Ogita and Siegfried M. Rump and Shin'ichi Oishi}, Journal = {Reliable Computing}, Year = {2010}, Month = {Jun}, Number = {1}, Pages = {24--45}, Volume = {14} } @Article{Monnet:2016:CIO, Title = {Computing an Inner and an Outer Approximation of the Viability Kernel}, Author = {D. Monnet and J. Ninin and Luc Jaulin}, Journal = {Reliable Computing}, Year = {2016}, Month = {Sep}, Number = {1}, Pages = {138--148}, Volume = {22} } @Article{Montan:2014:EMM, Title = {Efficient Matrix Multiplication Based on Discrete Stochastic Arithmetic}, Author = {Sethy Montan and Christophe Denis and Jean-Marie Chesneaux and Jean-Luc Lamotte}, Journal = {Reliable Computing}, Year = {2014}, Month = {Nov}, Number = {4}, Pages = {398--416}, Volume = {19} } @Article{Moore:2006:IRR, Title = {Introductory Remarks on Reliable Engineering Computing}, Author = {R. Moore}, Journal = {Reliable Computing}, Year = {2006}, Number = {6}, Pages = {405--408}, Volume = {12} } @Article{Moore:1999:D, Title = {The Dawning}, Author = {R. Moore}, Journal = {Reliable Computing}, Year = {1999}, Number = {4}, Pages = {423--424}, Volume = {5} } @Article{Moore:2002:SSF, Title = {Sparse Systems in Fixed Point Form}, Author = {R. E. Moore}, Journal = {Reliable Computing}, Year = {2002}, Number = {4}, Pages = {249--265}, Volume = {8} } @Article{Morales:1998:IMR, Title = {Interval Methods in Robot Navigation}, Author = {D. Morales and T. C. Son}, Journal = {Reliable Computing}, Year = {1998}, Number = {1}, Pages = {55--61}, Volume = {4} } @Article{Mrozek:1997:HCK, Title = {Heteroclinic connections in the {K}uramoto-{S}ivashinsky equation: a computer assisted proof}, Author = {M. Mrozek and M. Zelawski}, Journal = {Reliable Computing}, Year = {1997}, Number = {3}, Pages = {277--285}, Volume = {3} } @Article{Munoz:2004:SIG, Title = {Slope Intervals, Generalized Gradients, Semigradients, Slant Derivatives, and Csets}, Author = {H. Mu{\~n}oz and R. B. Kearfott}, Journal = {Reliable Computing}, Year = {2004}, Number = {3}, Pages = {163--193}, Volume = {4} } @Article{Muhanna:2007:IFE, Title = {Interval Finite Elements as a Basis for Generalized Models of Uncertainty in Engineering Mechanics}, Author = {R. L. Muhanna and H. Zhang and R. L. Mullen}, Journal = {Reliable Computing}, Year = {2007}, Number = {2}, Pages = {173--194}, Volume = {13} } @Article{Muller:1999:FRT, Title = {A Few Results on Table-Based Methods}, Author = {J.-M. Muller}, Journal = {Reliable Computing}, Year = {1999}, Number = {3}, Pages = {279--288}, Volume = {5} } @Article{Goubault:2013:GIA, Title = {General Inner Approximation of Vector--valued Functions}, Author = {Olivier Mullier and {\'E}ric Goubault and Michel Kieffer and Sylvie Putot}, Journal = {Reliable Computing}, Year = {2013}, Month = {Nov}, Number = {1}, Pages = {117--143}, Volume = {18} } @Article{Musaev:1992:ARC, Title = {An approach to reliable computations with the minimal representation}, Author = {E. A. Musaev}, Journal = {Interval Computations}, Year = {1992}, Number = {4}, Pages = {37--41} } @Article{Musaev:1992:WCT, Title = {Wave computations. {A} technique for optimal quasi-concurrent self-validation}, Author = {E. A. Musaev}, Journal = {Interval Computations}, Year = {1992}, Number = {1}, Pages = {53--60} } @Article{Musaev:1991:NIP, Title = {Narrowing of intervals by partial derivatives}, Author = {E. A. Musaev}, Journal = {Interval Computations}, Year = {1991}, Number = {1}, Pages = {86--91} } @Article{Nadezhin:2014:JL, Title = {{JI}nterval Library: {P}rinciples, Development, and Perspectives}, Author = {Dmitry Yu. Nadezhin and Sergei I. Zhilin}, Journal = {Reliable Computing}, Year = {2014}, Month = {Jan}, Number = {3}, Pages = {229--247}, Volume = {19} } @Article{Nakamura:1993:GIK, Title = {Guaranteed Intervals for {K}olmogorov's Theorem (and Their Possible Relation to Neural Networks)}, Author = {M. Nakamura and R. Mines and V. Kreinovich}, Journal = {Interval Computations}, Year = {1993}, Number = {3}, Pages = {183--199} } @Article{Nakao:1994:NVS, Title = {Numerical Verifications of Solutions for Nonlinear Hyperbolic Equations}, Author = {M. T. Nakao}, Journal = {Interval Computations}, Year = {1994}, Number = {4}, Pages = {64--77} } @Article{Nakao:2003:SCA, Title = {Some Computer Assisted Proofs for Solutions of the Heat Convection Problems}, Author = {M. T. Nakao and Y. Watanabe and N. Yamamoto and T. Nishida}, Journal = {Reliable Computing}, Year = {2003}, Number = {5}, Pages = {359--372}, Volume = {9} } @Article{Nakao:1998:CLE, Title = {Constructive {$L^2$} Error Estimates for Finite Element Solutions of the {S}tokes Equations}, Author = {M. T. Nakao and N. Yamamoto and Y. Watanabe}, Journal = {Reliable Computing}, Year = {1998}, Number = {2}, Pages = {115--124}, Volume = {4} } @Article{Narinyani:1992:NNP, Title = {Ne-factors and natural pragmatics: what do the intervals represent}, Author = {A. S. Narinyani}, Journal = {Interval Computations}, Year = {1992}, Number = {4}, Pages = {42--47} } @Article{Narkawicz:2012:BRR, Title = {Bounding the Range of a Rational Function over a Box}, Author = {Anthony Narkawicz and J{\"{u}}rgen Garloff and Andrew P. Smith and C{\'{e}}sar A. Mu{\~{n}}oz}, Journal = {Reliable Computing}, Year = {2012}, Month = {Dec}, Number = {1}, Pages = {34--39}, Volume = {17} } @Article{Narkawicz:2012:FVC, Title = {Formal Verification of Conflict Detection Algorithms for Arbitrary Trajectories}, Author = {Anthony Narkawicz and C{\'{e}}sar A. Mu{\~{n}}oz}, Journal = {Reliable Computing}, Year = {2012}, Month = {Dec}, Number = {2}, Pages = {209--237}, Volume = {17} } @Article{Nataraj:2011:INM, Title = {An Interval Newton Method Based on the {B}ernstein Form for Bounding the Zeros of Polynomial Systems}, Author = {P. S. V. Nataraj and M. Arounassalame}, Journal = {Reliable Computing}, Year = {2011}, Month = {Jun}, Number = {2}, Pages = {109--119}, Volume = {15} } @Article{Nataraj:2003:RCF, Title = {Reliable Computation of Frequency Response Plots for Nonrational Transfer Functions to Prescribed Accuracy}, Author = {P. S. V. Nataraj and J. J. Barve}, Journal = {Reliable Computing}, Year = {2003}, Number = {5}, Pages = {373--389}, Volume = {9} } @Article{Nataraj:2004:GOH, Title = {Global Optimization with Higher Order Inclusion Function Forms. Part 1: A Combined Taylor-{Bernstein} Form}, Author = {P. S. V. Nataraj and K. Kotecha}, Journal = {Reliable Computing}, Year = {2004}, Number = {1}, Pages = {27--44}, Volume = {10} } @Article{Nataraj:2003:HOC, Title = {Higher Order Convergence for Multidimensional Functions with a New {T}aylor-{B}ernstein Form as Inclusion Function}, Author = {P. S. V. Nataraj and K. Kotecha}, Journal = {Reliable Computing}, Year = {2003}, Number = {3}, Pages = {185--203}, Volume = {9} } @Article{Nataraj:2002:PVC, Title = {A Parallelized Version of the Covering Algorithm for Solving Parameter-Dependent Systems of Nonlinear Equations}, Author = {P. S. V. Nataraj and A. K. Prakash}, Journal = {Reliable Computing}, Year = {2002}, Number = {2}, Pages = {123--130}, Volume = {8} } @Article{Nataraj:2002:NSS, Title = {A New Subdivision Strategy for Range Computations}, Author = {P. S. V. Nataraj and S. M. Sheela}, Journal = {Reliable Computing}, Year = {2002}, Number = {1}, Pages = {83--92}, Volume = {8} } @Article{Nataraj:2002:QPG, Title = {A {QFT} Procedure for Generating Design Frequencies and Bounds of Guaranteed Accuracy}, Author = {P. S. V. Nataraj and S. M. Sheela}, Journal = {Reliable Computing}, Year = {2002}, Number = {6}, Pages = {427--451}, Volume = {8} } @Article{Nataraj:2011:ETM, Title = {The Extrapolated {T}aylor Model}, Author = {P. S. V. Nataraj and Shanta Sondur}, Journal = {Reliable Computing}, Year = {2011}, Month = {Jul}, Number = {3}, Pages = {251--278}, Volume = {15} } @Article{Nataraj:1999:SRS, Title = {Synthesis of Robustly Stabilizing General Order Compensators for Interval Plants Using Interval Analysis}, Author = {P. S. V. Nataraj and S. Srivastava}, Journal = {Reliable Computing}, Year = {1999}, Number = {4}, Pages = {407--422}, Volume = {5} } @Article{Nedialkov:1999:IHO, Title = {An Interval Hermite-Obreschkoff Method for Computing Rigorous Bounds on the Solution of an Initial Value Problem for an Ordinary Differential Equation}, Author = {N. S. Nedialkov and K. R. Jackson}, Journal = {Reliable Computing}, Year = {1999}, Number = {3}, Pages = {289--310}, Volume = {5} } @Article{Nedialkov:2016:BMV, Title = {On the Blunting Method in Verified Integration of {ODE}s}, Author = {Nedialko S. Nedialkov and Kenneth R. Jackson and Markus Neher}, Journal = {Reliable Computing}, Year = {2016}, Month = {Jul}, Number = {1}, Pages = {15--34}, Volume = {23} } @Article{Nedialkov:1999:EHO, Title = {An Effective High-Order Interval Method for Validating Existence and Uniqueness of the Solution of an IVP for an ODE}, Author = {N. S. Nedialkov and K. R. Jackson and J. D. Pryce}, Journal = {Reliable Computing}, Year = {2001}, Number = {6}, Pages = {449--465}, Volume = {7} } @Article{Nedoma:1997:SSS, Title = {Sign-Stable Solutions of Column-Vague Linear Equation Systems}, Author = {J. Nedoma}, Journal = {Reliable Computing}, Year = {1997}, Number = {2}, Pages = {173--180}, Volume = {3} } @Article{Neher:2001:VBT, Title = {Validated Bounds for Taylor Coefficients of Analytic Functions}, Author = {M. Neher}, Journal = {Reliable Computing}, Year = {2001}, Number = {4}, Pages = {307--319}, Volume = {7} } @Article{Nehmeier:2011:FET, Title = {filib++ Expression Templates and the Coming Interval Standard}, Author = {M. Nehmeier and J{\"{u}}rgen {Wolff von Gudenberg}}, Journal = {Reliable Computing}, Year = {2011}, Month = {Jul}, Number = {4}, Pages = {312--320}, Volume = {15} } @Article{Nenov:2003:IMA, Title = {Interval Methods for Accelerated Global Search in the {M}icrosoft {Excel} {S}olver}, Author = {I. P. Nenov and D. H. Fylstra}, Journal = {Reliable Computing}, Year = {2003}, Number = {2}, Pages = {143--159}, Volume = {9} } @Article{Nesterov:1997:ITA, Title = {Interval and Twin Arithmetics}, Author = {V. M. Nesterov}, Journal = {Reliable Computing}, Year = {1997}, Number = {4}, Pages = {369--380}, Volume = {3} } @Article{Nesterov:1993:UMT, Title = {How To Use Monotonicity-Type Information To Get Better Estimates of the Range of Real-Valued Functions}, Author = {V. M. Nesterov}, Journal = {Interval Computations}, Year = {1993}, Number = {4}, Pages = {3--12} } @Article{Nesterov:1992:ERV, Title = {Estimating a range of values of functions using extended interval arithmetics}, Author = {V. M. Nesterov}, Journal = {Interval Computations}, Year = {1992}, Number = {4}, Pages = {48--53} } @Article{Neumaier:2004:CFS, Title = {Clouds, Fuzzy Sets, and Probability Intervals}, Author = {A. Neumaier}, Journal = {Reliable Computing}, Year = {2004}, Number = {4}, Pages = {249--272}, Volume = {10} } @Article{Neumaier:2003:TFU, Title = {{T}aylor Forms - Use and Limits}, Author = {A. Neumaier}, Journal = {Reliable Computing}, Year = {2003}, Number = {1}, Pages = {43--79}, Volume = {9} } @Article{Neumaier:2002:GCS, Title = {Grand Challenges and Scientific Standards in Interval Analysis}, Author = {A. Neumaier}, Journal = {Reliable Computing}, Year = {2002}, Number = {4}, Pages = {313--320}, Volume = {8} } @Article{Neumaier:2000:SDH, Title = {Erratum to: A Simple Derivation of the {H}ansen-{B}liek-{R}ohn-{N}ing-{K}earfott Enclosure for Linear Interval Equations (Reliable Computing Vol. 5 (2) (1999))}, Author = {A. Neumaier}, Journal = {Reliable Computing}, Year = {2000}, Number = {2}, Pages = {227}, Volume = {6} } @Article{Neumaier:1999:SDH, Title = {A Simple Derivation of the {H}ansen-{B}liek-{R}ohn-{N}ing-{K}earfott Enclosure for Linear Interval Equations}, Author = {A. Neumaier}, Journal = {Reliable Computing}, Year = {1999}, Number = {2}, Pages = {131--136}, Volume = {5} } @Article{Neumaier:2007:LSL, Title = {Linear Systems with Large Uncertainties, with Applications to Truss Structures}, Author = {A. Neumaier and A. Pownuk}, Journal = {Reliable Computing}, Year = {2007}, Number = {2}, Pages = {149--172}, Volume = {13} } @Article{Nguyen:1995:NIS, Title = {From Numerical Intervals to Set Intervals (Interval-Related Results Presented at the First International Workshop on Applications and Theory of Random Sets)}, Author = {H. T. Nguyen and V. Kreinovich}, Journal = {Reliable Computing}, Year = {1995}, Number = {1}, Pages = {95--102}, Volume = {3} } @Article{Nguyen:1995:ILN, Title = {Interpolation that leads to the narrowest intervals and its application to expert systems and intelligent control}, Author = {H. T. Nguyen and V. Kreinovich and B. Lea and D. Tolber}, Journal = {Reliable Computing}, Year = {1995}, Number = {3}, Pages = {299--316}, Volume = {1} } @Article{Nguyen:2004:DPL, Title = {Dirty Pages of Logarithm Tables, Lifetime of the Universe, and (Subjective) Probabilities on Finite and Infinite Intervals}, Author = {H. T. Nguyen and V. Kreinovich and L. Longpre}, Journal = {Reliable Computing}, Year = {2004}, Number = {2}, Pages = {83--106}, Volume = {10} } @Article{Nogueira:1997:IRT, Title = {Interval-Related Talks at {NASA} {URC} Conference}, Author = {M. Nogueira}, Journal = {Reliable Computing}, Year = {1997}, Number = {4}, Pages = {459--460}, Volume = {3} } @Article{Nogueira:1998:WIB, Title = {Why Intervals? Because If We Allow Other Sets, Tractable Problems Become Intractable}, Author = {M. Nogueira and A. Nandigam}, Journal = {Reliable Computing}, Year = {1998}, Number = {4}, Pages = {389--394}, Volume = {4} } @Article{Noubir:1996:SCP, Title = {Self-correcting polynomial programs}, Author = {G. Noubir and H. J. Nussbaumer}, Journal = {Reliable Computing}, Year = {1996}, Number = {2}, Pages = {139--146}, Volume = {2} } @Article{Oberman:1996:RDL, Title = {Reducing division latency with reciprocal caches}, Author = {S. F. Oberman and M. J. Flynn}, Journal = {Reliable Computing}, Year = {1996}, Number = {2}, Pages = {147--154}, Volume = {2} } @Article{Ogita:2005:FII, Title = {Fast Inclusion of Interval Matrix Multiplication}, Author = {T. Ogita and S. Oishi}, Journal = {Reliable Computing}, Year = {2005}, Number = {3}, Pages = {191--205}, Volume = {11} } @Article{Oberman:2003:CSR, Title = {Computation of Sharp Rigorous Componentwise Error Bounds for the Approximate Solutions of Systems of Linear Equations}, Author = {T. Ogita and S. Oishi and Y. Ushiro}, Journal = {Reliable Computing}, Year = {2003}, Number = {3}, Pages = {229--239}, Volume = {9} } @Article{Ohta:2000:NPI, Title = {Nonconvex Polygon Interval Arithmetic as a Tool for the Analysis and Design of Robust Control Systems}, Author = {Y. Ohta}, Journal = {Reliable Computing}, Year = {2000}, Number = {3}, Pages = {247--279}, Volume = {6} } @Article{Okayama:2013:EEE, Title = {Error Estimates with Explicit Constants for Sinc Quadrature and Sinc Indefinite Integration over Infinite Intervals}, Author = {Tomoaki Okayama}, Journal = {Reliable Computing}, Year = {2013}, Month = {Nov}, Number = {1}, Pages = {45--65}, Volume = {19} } @Article{Oliveira:1996:NSM, Title = {New slope methods for sharper interval functions and a note on {F}ischer's acceleration method}, Author = {J. B. Oliveira}, Journal = {Reliable Computing}, Year = {1996}, Number = {3}, Pages = {299--320}, Volume = {2} } @Article{Oliveira:2003:RAO, Title = {Robust Approximation of Offsets, Bisectors, and Medial Axes of Plane Curves}, Author = {J. B. Oliveira and L. H. de Figueiredo}, Journal = {Reliable Computing}, Year = {2003}, Number = {2}, Pages = {161--175}, Volume = {9} } @Article{Oliveira:2002:ICV, Title = {Interval Computation of {V}iswanath's Constant}, Author = {J. B. Oliveira and L. Henrique de Figueiredo}, Journal = {Reliable Computing}, Year = {2002}, Number = {2}, Pages = {131--138}, Volume = {8} } @Article{Orlov:1992:IS, Title = {Interval statistics}, Author = {A. I. Orlov}, Journal = {Interval Computations}, Year = {1992}, Number = {1}, Pages = {44--52} } @Article{Ostylovsky:1995:EAV, Title = {An estimate of the absolute value and width of the solution of a linear system of equations with tridiagonal interval matrix by the interval sweep method}, Author = {A. N. Ostylovsky}, Journal = {Reliable Computing}, Year = {1995}, Number = {4}, Pages = {393--402}, Volume = {1} } @Article{Otten:1997:AEE, Title = {Approximation Error and Error Accumulation for the Landen Transform}, Author = {W. Otten and W. Luther}, Journal = {Reliable Computing}, Year = {1997}, Number = {3}, Pages = {249--258}, Volume = {3} } @Article{Paluh:1991:AIM, Title = {Application of interval mathematics for solving technical diagnostics tasks of non-stop manufacture in chemical industry}, Author = {B. V. Paluh and B. V. Vasilyov and V. L. Perov}, Journal = {Interval Computations}, Year = {1991}, Number = {1}, Pages = {99--104} } @Article{Paluh:2007:ERC, Title = {Experiments with Range Computations Using Extrapolation}, Author = {N. S. V. Paluri and S. Sondur}, Journal = {Reliable Computing}, Year = {2007}, Number = {1}, Pages = {1--23}, Volume = {13} } @Article{Pankov:1992:PFD, Title = {Proof of finite-dimensional inequalities by means of interval analysis}, Author = {P. S. Pankov}, Journal = {Interval Computations}, Year = {1992}, Number = {2}, Pages = {30--38} } @Article{Pankov:1992:UIM, Title = {Using interval methods in cluster analysis and verified representation of connected sets}, Author = {P. S. Pankov and B. D. Bayachorova}, Journal = {Interval Computations}, Year = {1992}, Number = {4}, Pages = {54--58} } @Article{Pankova:1992:PSA, Title = {Programming support and algorithmic language for validating computations on {ES} ({IBM} 360/370) series computer}, Author = {G. D. Pankova}, Journal = {Interval Computations}, Year = {1992}, Number = {1}, Pages = {86--95} } @Article{Panyukov:2014:SAA, Title = {Scalability of Algorithms for Arithmetic Operations in Radix Notation}, Author = {Anatoly V. Panyukov}, Journal = {Reliable Computing}, Year = {2014}, Month = {Nov}, Number = {4}, Pages = {417--434}, Volume = {19} } @Article{Panyukov:2013:CBP, Title = {Computing Best Possible Pseudo--Solutions to Interval Linear Systems of Equations}, Author = {Anatoly V. Panyukov and Valentin A. Golodov}, Journal = {Reliable Computing}, Year = {2013}, Month = {Dec}, Number = {2}, Pages = {215--228}, Volume = {19} } @Article{Patre:2006:RCT, Title = {Robust Control for Two-Time-Scale Discrete Interval Systems}, Author = {B. M. Patre and B. Bandyopadhyay}, Journal = {Reliable Computing}, Year = {2006}, Number = {1}, Pages = {45--58}, Volume = {12} } @Article{Patre:2010:RSF, Title = {Robust State Feedback for Interval Systems: {A}n Interval Analysis Approach}, Author = {B. M. Patre and P. J. Deore}, Journal = {Reliable Computing}, Year = {2010}, Month = {Jun}, Number = {1}, Pages = {46--60}, Volume = {14} } @Article{Pelessoni:2003:CIP, Title = {Convex Imprecise Previsions}, Author = {R. Pelessoni and P. Vicig}, Journal = {Reliable Computing}, Year = {2003}, Number = {6}, Pages = {465--485}, Volume = {9} } @Article{Pereira:2006:UTB, Title = {Uncertainty in Thermal Basin Modeling: An Interval Finite Element Approach}, Author = {S. C. Pereira and U. T. Mello and N. F. F. Ebecken and R. L. Muhanna}, Journal = {Reliable Computing}, Year = {2006}, Number = {6}, Pages = {451--470}, Volume = {12} } @Article{Perepelitsa:1993:IDM, Title = {Interval discrete models and multiobjectivity complexity estimates}, Author = {V. A. Perepelitsa and G. L. Kozina}, Journal = {Interval Computations}, Year = {1993}, Number = {1}, Pages = {51--59} } @Article{Pesonen:1996:IAC, Title = {Interval approach challenges {M}onte {C}arlo simulation}, Author = {J. Pesonen and E. Hyvonen}, Journal = {Reliable Computing}, Year = {1996}, Number = {2}, Pages = {155--160}, Volume = {2} } @Article{Petkovic:2011:CAI, Title = {Computational Aspects of the Implementation of Disk Inversions}, Author = {Ivan Petkovi{\'{c}}}, Journal = {Reliable Computing}, Year = {2011}, Month = {Jun}, Number = {2}, Pages = {81--90}, Volume = {15} } @Article{Petkovic:2011:HOM, Title = {Higher Order Methods for the Inclusion of Multiple Zeros of Polynomials}, Author = {Miodrag S. Petkovi{\'{c}} and Du\v{s}an M. Milo{\v{s}}evi{\'{c}}}, Journal = {Reliable Computing}, Year = {2011}, Month = {Jun}, Number = {2}, Pages = {91--108}, Volume = {15} } @Article{Petkovic:1995:VMI, Title = {Verification methods for inclusion disks}, Author = {L. D. Petkovic and M. Trajkovic}, Journal = {Reliable Computing}, Year = {1995}, Number = {4}, Pages = {403--410}, Volume = {1} } @Article{Petvokic:1993:SOI, Title = {On some optimal inclusion approximations by discs}, Author = {L. D. Petkovic and M. Trajkovic}, Journal = {Interval Computations}, Year = {1993}, Number = {1}, Pages = {34--50} } @Article{Petkovic:1997:SMH, Title = {Slope Methods of Higher Order for the Inclusion of Complex Roots of Polynomials}, Author = {L. D. Petkovic and S. Trickovic and M. S. Petkovic}, Journal = {Reliable Computing}, Year = {1997}, Number = {4}, Pages = {349--362}, Volume = {3} } @Article{Petkovic:2004:OLM, Title = {{O}strowski-like Method with Corrections for the Inclusion of Polynomial Zeros}, Author = {M. S. Petkovic and D. M. Milosevic}, Journal = {Reliable Computing}, Year = {2004}, Number = {6}, Pages = {437--467}, Volume = {10} } @Article{Plotnikov:1998:OCE, Title = {One Criterion of Existence of a {H}amiltonian Cycle}, Author = {A. D. Plotnikov}, Journal = {Reliable Computing}, Year = {1998}, Number = {2}, Pages = {199--202}, Volume = {4} } @Article{Plum:1994:ESP, Title = {Enclosures for Solutions of Parameter-Dependent Nonlinear Elliptic Boundary Value Problems: Theory and Implementation on a Parallel Computer}, Author = {M. Plum}, Journal = {Interval Computations}, Year = {1994}, Number = {3}, Pages = {106--121} } @Article{Podchukayev:1994:AMC, Title = {An Analytical Method of Constructing {H}urwitz Interval Polynomials}, Author = {V. A. Podchukayev and I. M. Svetlov}, Journal = {Interval Computations}, Year = {1994}, Number = {2}, Pages = {52--67} } @Article{Popov:1998:RMI, Title = {A Relation Between Morphological and Interval Operations}, Author = {A. T. Popov}, Journal = {Reliable Computing}, Year = {1998}, Number = {2}, Pages = {167--178}, Volume = {4} } @Article{Popov:1998:AFM, Title = {An Application of Fuzzy Mathematical Morphology to Interval-Valued Knowledge Representation: A Remark}, Author = {A. T. Popov and H. T. Nguyen and L. K. Reznik}, Journal = {Reliable Computing}, Year = {1998}, Number = {3}, Pages = {283--290}, Volume = {4} } @Article{Popova:2001:MDP, Title = {Multiplication Distributivity of Proper and Improper Intervals}, Author = {E. D. Popova}, Journal = {Reliable Computing}, Year = {2001}, Number = {2}, Pages = {129--140}, Volume = {7} } @Article{Popova:1996:IOI, Title = {Interval operations involving {NaNs}}, Author = {E. D. Popova}, Journal = {Reliable Computing}, Year = {1996}, Number = {2}, Pages = {161--166}, Volume = {2} } @Article{Popova:1994:EIA, Title = {Extended Interval Arithmetic in {IEEE} Floating-Point Environment}, Author = {E. D. Popova}, Journal = {Interval Computations}, Year = {1994}, Number = {4}, Pages = {100--129} } @Article{Pownuk:2013:CMI, Title = {Checking Monotonicity is {NP}--Hard Even for Cubic Polynomials}, Author = {Andrzej Pownuk and Luc Longpr{\'e} and Vladik Kreinovich}, Journal = {Reliable Computing}, Year = {2013}, Month = {Jul}, Number = {1}, Pages = {90--96}, Volume = {18} } @Article{Pownuk:2011:AOP, Title = {Application of Order-Preserving Functions to the Modeling of Computational Mechanics Problems with Uncertainty}, Author = {Andrzej Pownuk and Naveen Kumar Goud Ramunigari}, Journal = {Reliable Computing}, Year = {2011}, Month = {Jun}, Number = {2}, Pages = {132--143}, Volume = {15} } @Article{Prolubnikov:2013:IAT, Title = {An Interval Approach to Pattern Recognition of Numerical Matrices}, Author = {Alexander V. Prolubnikov}, Journal = {Reliable Computing}, Year = {2013}, Month = {Nov}, Number = {1}, Pages = {107--119}, Volume = {19} } @Article{Provetti:1996:OEI, Title = {Ordering events: Intervals are sufficient, more general sets are usually not necessary}, Author = {A. Provetti}, Journal = {Reliable Computing}, Year = {1996}, Number = {3}, Pages = {321--328}, Volume = {2} } @Article{Puig:2003:WCS, Title = {Worst-Case Simulation of Discrete Linear Time-Invariant Interval Dynamic Systems}, Author = {V. Puig and J. Saludes and J. Quevedo}, Journal = {Reliable Computing}, Year = {2003}, Number = {4}, Pages = {251--290}, Volume = {9} } @Article{Pushkarev:2013:MSD, Title = {Maximizing Stability Degree of Control Systems under Interval Uncertainty Using a Coefficient Method}, Author = {Maxim I. Pushkarev and Sergey A. Gaivoronsky}, Journal = {Reliable Computing}, Year = {2013}, Month = {Dec}, Number = {3}, Pages = {248--260}, Volume = {19} } @Article{Pushkov:2005:BRM, Title = {Boundary Realizations Method for Interval Linear Dynamic Systems}, Author = {S. G. Pushkov and S. Y. Kalinkina}, Journal = {Reliable Computing}, Year = {2005}, Number = {5}, Pages = {413--423}, Volume = {11} } @Article{Rall:2016:IDA, Title = {Interval Divided--Difference Arithmetic}, Author = {Louis B. Rall}, Journal = {Reliable Computing}, Year = {2016}, Month = {Jul}, Number = {1}, Pages = {154--162}, Volume = {23} } @Article{Rall:2003:EFG, Title = {Evaluation of Functions, Gradients, and {J}acobians}, Author = {L. B. Rall}, Journal = {Reliable Computing}, Year = {2003}, Number = {2}, Pages = {177--182}, Volume = {9} } @Article{Rall:2000:II, Title = {Interval Integration}, Author = {L. B. Rall}, Journal = {Reliable Computing}, Year = {2000}, Number = {1}, Pages = {93--94}, Volume = {6} } @Article{Ratschan:2002:AQC, Title = {Approximate Quantified Constraint Solving by Cylindrical Box Decomposition}, Author = {S. Ratschan}, Journal = {Reliable Computing}, Year = {2002}, Number = {1}, Pages = {21--42}, Volume = {8} } @Article{Ratschek:2000:ISI, Title = {Introduction to the Special Issue: What Can One Learn from Box-Plane Intersections?}, Author = {H. Ratschek and J. G. Rokne}, Journal = {Reliable Computing}, Year = {2000}, Number = {1}, Pages = {1--8}, Volume = {6} } @Article{Ratschek:1995:FWI, Title = {Formulas for the width of interval products}, Author = {H. Ratschek and J. G. Rokne}, Journal = {Reliable Computing}, Year = {1995}, Number = {1}, Pages = {9--14}, Volume = {1} } @Article{Rauh:2011:VSO, Title = {Verified Simulation of {ODEs} and {DAEs} in {ValEncIA-IVP}}, Author = {Andreas Rauh and Ekaterina Auer}, Journal = {Reliable Computing}, Year = {2011}, Month = {Jul}, Number = {4}, Pages = {370--381}, Volume = {15} } @Article{Rauh:2011:DRO, Title = {Detection and Reduction of Overestimation in Guaranteed Simulations of {H}amiltonian Systems}, Author = {Andreas Rauh and Ekaterina Auer and Mareile Freihold and Eberhard P. Hofer and Harald Aschemann}, Journal = {Reliable Computing}, Year = {2011}, Month = {Jul}, Number = {4}, Pages = {321--332}, Volume = {15} } @Article{Rauh:2011:ROC, Title = {Robust and Optimal Control of Uncertain Dynamical Systems with State-Dependent Switchings Using Interval Arithmetic}, Author = {Andreas Rauh and Johanna Minisini and Eberhard P. Hofer and Harald Aschemann}, Journal = {Reliable Computing}, Year = {2011}, Month = {Jul}, Number = {4}, Pages = {333--344}, Volume = {15} } @Article{Rauh:2014:NVE, Title = {Numerical Verification and Experimental Validation of Sliding Mode Control Design for Uncertain Thermal {SOFC} Models}, Author = {Andreas Rauh and Luise Senkel and Thomas D{\"o}vtschel and Harald Aschemann and Ekaterina Auer}, Journal = {Reliable Computing}, Year = {2014}, Month = {May}, Number = {4}, Pages = {330--350}, Volume = {19} } @Article{Rauh:2014:IMS, Title = {Interval Methods for Sensitivity--Based Model--Predictive Control of Solid Oxide Fuel Cell Systems}, Author = {Andreas Rauh and Luise Senkel and Julia Kersten and Harald Aschemann}, Journal = {Reliable Computing}, Year = {2014}, Month = {Jun}, Number = {4}, Pages = {361--384}, Volume = {19} } @Article{Rauh:2013:EET, Title = {Exponential Enclosure Techniques for the Computation of Guaranteed State Enclosures in {ValEncIA}--{IVP}}, Author = {Andreas Rauh and Ramona Westphal and Harald Aschemann and Ekaterina Auer}, Journal = {Reliable Computing}, Year = {2013}, Month = {Nov}, Number = {1}, Pages = {66--90}, Volume = {19} } @Article{Ray:2012:MME, Title = {A Matrix Method for Efficient Computation of {B}ernstein Coefficients}, Author = {Shashwati Ray and P. S. V. Nataraj}, Journal = {Reliable Computing}, Year = {2012}, Month = {Dec}, Number = {1}, Pages = {40--71}, Volume = {17} } @Article{Ray:2010:NSS, Title = {A New Strategy for Selecting Subdivision Point in the {B}ernstein Approach to Polynomial Optimization}, Author = {Shashwati Ray and P. S. V. Nataraj}, Journal = {Reliable Computing}, Year = {2010}, Month = {Jun}, Number = {1}, Pages = {117--137}, Volume = {14} } @Article{Revol:2005:MAP, Title = {Motivations for an Arbitrary Precision Interval Arithmetic and the MPFI Library}, Author = {N. Revol and F. Rouillier}, Journal = {Reliable Computing}, Year = {2005}, Number = {4}, Pages = {275--290}, Volume = {11} } @Article{Revol:2013:PII, Title = {Parallel Implementation of Interval Matrix Multiplication}, Author = {Nathalie Revol and Philippe Th{\'e}veny}, Journal = {Reliable Computing}, Year = {2013}, Month = {Nov}, Number = {1}, Pages = {91--106}, Volume = {19} } @Article{Revol:2000:ASA, Title = {Accelerated Shift-and-Add Algorithms}, Author = {N. Revol and J.-C. Yakoubsohn }, Journal = {Reliable Computing}, Year = {2000}, Number = {2}, Pages = {193--205}, Volume = {6} } @Article{Rohn:2016:TCE, Title = {Theoretical Characterization of Enclosures}, Author = {Jiri Rohn}, Journal = {Reliable Computing}, Year = {2016}, Month = {Oct}, Number = {1}, Pages = {140--145}, Volume = {21} } @Article{Rohn:2015:SSI, Title = {The Solution Set of Interval Linear Equations is Homeomorphic to the Unit Cube: {A}n Explicit Construction}, Author = {Jiri Rohn}, Journal = {Reliable Computing}, Year = {2015}, Month = {Nov}, Number = {1}, Pages = {25--34}, Volume = {21} } @Article{Rohn:2006:RIM, Title = {Regularity of Interval Matrices and Theorems of the Alternatives}, Author = {J. Rohn}, Journal = {Reliable Computing}, Year = {2006}, Number = {2}, Pages = {99--105}, Volume = {12} } @Article{Rohn:2005:HSS, Title = {How Strong Is Strong Regularity?}, Author = {J. Rohn}, Journal = {Reliable Computing}, Year = {2005}, Number = {6}, Pages = {491--493}, Volume = {11} } @Article{Rohn:2005:LIE, Title = {Linear Interval Equations: Midpoint Preconditioning May Produce a 100% Overestimation for Arbitrarily Narrow Data Even in Case n=4}, Author = {J. Rohn}, Journal = {Reliable Computing}, Year = {2005}, Number = {2}, Pages = {129--135}, Volume = {11} } @Article{Rohn:2005:NFS, Title = {A Normal Form Supplement to the Oettli-Prager Theorem}, Author = {J. Rohn}, Journal = {Reliable Computing}, Year = {2005}, Number = {1}, Pages = {35--39}, Volume = {11} } @Article{Rohn:1997:CSL, Title = {Complexity of Some Linear Problems with Interval Data}, Author = {J. Rohn}, Journal = {Reliable Computing}, Year = {1997}, Number = {3}, Pages = {315--323}, Volume = {3} } @Article{Rohn:1997:OPI, Title = {On Overestimations Produced by the Interval Gaussian Algorithm (Dedicated to {P}rof. {D}r. {G}erhard {H}eindl on the occasion of his 60th birthday)}, Author = {J. Rohn}, Journal = {Reliable Computing}, Year = {1997}, Number = {4}, Pages = {363--368}, Volume = {3} } @Article{Rohn:1996:ESO, Title = {Enclosing solutions of overdetermined systems of linear interval equations}, Author = {J. Rohn}, Journal = {Reliable Computing}, Year = {1996}, Number = {2}, Pages = {167--172}, Volume = {2} } @Article{Rohn:1993:CTB, Title = {Cheap and Tight Bounds: The Recent Result by {E}. {H}ansen Can Be Made More Efficient}, Author = {J. Rohn}, Journal = {Interval Computations}, Year = {1993}, Number = {4}, Pages = {13--21} } @Article{Roy:2011:GOS, Title = {Global Optimization and Singular Nonlinear Programs: {N}ew Techniques}, Author = {Julie Roy and R. Baker Kearfott}, Journal = {Reliable Computing}, Year = {2011}, Month = {Jul}, Number = {3}, Pages = {242--250}, Volume = {15} } @Article{Rueher:1997:CCS, Title = {Concurent Cooperating Solvers on the Reals}, Author = {M. Rueher and C. Solnon}, Journal = {Reliable Computing}, Year = {1997}, Number = {3}, Pages = {325--333}, Volume = {3} } @Article{Rump:2014:VBP, Title = {Verified Bounds for the $p$--Norm Condition Number}, Author = {Siegfried M. Rump}, Journal = {Reliable Computing}, Year = {2014}, Month = {Jun}, Number = {1}, Pages = {45--52}, Volume = {20} } @Article{Rump:1998:NEI, Title = {A Note on Epsilon-Inflation}, Author = {S. M. Rump}, Journal = {Reliable Computing}, Year = {1998}, Number = {4}, Pages = {371--375}, Volume = {4} } @Article{Rump:1992:ISL, Title = {Inclusion of the solution for large linear systems with {M}-matrix}, Author = {S. M. Rump}, Journal = {Interval Computations}, Year = {1992}, Number = {1}, Pages = {22--43} } @Article{Rump:1992:IZN, Title = {Inclusion of Zeros of Nowhere Differentiable {n}-Dimensional Functions}, Author = {S. M. Rump}, Journal = {Reliable Computing}, Year = {1992}, Number = {1}, Pages = {5--16}, Volume = {3} } @Article{Sainudiin:2013:RES, Title = {A Rigorous Extension of the {S}ch{\"o}nhage--{S}trassen Integer Multiplication Algorithm Using Complex Interval Arithmetic}, Author = {Raazesh Sainudiin and Thomas Steinke}, Journal = {Reliable Computing}, Year = {2013}, Month = {Sep}, Number = {1}, Pages = {97--116}, Volume = {18} } @Article{Sainudiin:2013:ATU, Title = {An Auto--Validating, Trans--Dimensional, Universal Rejection Sampler for Locally {L}ipschitz Arithmetical Expressions}, Author = {Raazesh Sainudiin and Thomas York}, Journal = {Reliable Computing}, Year = {2013}, Month = {Apr}, Number = {1}, Pages = {15--54}, Volume = {18} } @Article{Sainz:2002:FSS, Title = {Formal Solution to Systems of Interval Linear or Non-Linear Equations}, Author = {M. A. Sainz and E. Gardenyes and L. Jorba}, Journal = {Reliable Computing}, Year = {2002}, Number = {3}, Pages = {189--211}, Volume = {8} } @Article{Sainz:2002:IES, Title = {Interval Estimations of Solution Sets to Real-Valued Systems of Linear or Non-Linear Equations}, Author = {M. A. Sainz and E. Gardenyes and L. Jorba}, Journal = {Reliable Computing}, Year = {2002}, Number = {4}, Pages = {283--305}, Volume = {8} } @Article{Sakurai:2000:FAF, Title = {On Factorization of Analytic Functions and Its Verification}, Author = {T. Sakurai and H. Sugiura}, Journal = {Reliable Computing}, Year = {2000}, Number = {4}, Pages = {459--470}, Volume = {6} } @Article{Salama:2005:ISS, Title = {Interval Schemes for Singularly Perturbed Initial Value Problems}, Author = {A. A. Salama and E. Hamdy}, Journal = {Reliable Computing}, Year = {2005}, Number = {1}, Pages = {41--48}, Volume = {11} } @Article{Saraev:2013:IPM, Title = {Interval Pseudo--Inverse Matrices and Interval {G}reville Algorithm}, Author = {Pavel V. Saraev}, Journal = {Reliable Computing}, Year = {2013}, Month = {Dec}, Number = {1}, Pages = {147--156}, Volume = {18} } @Article{Savchenko:2014:CPA, Title = {Computation of Potential and Attraction Force of an Ellipsoid}, Author = {Alexander Savchenko}, Journal = {Reliable Computing}, Year = {2014}, Month = {Apr}, Number = {3}, Pages = {318--329}, Volume = {19} } @Article{Schaefer:1993:PZA, Title = {Precise Zeros of Analytic Functions Using Interval Arithmetic}, Author = {M. J. Schaefer}, Journal = {Interval Computations}, Year = {1993}, Number = {4}, Pages = {22--39} } @Article{Schaefer:1995:PCZ, Title = {A parallel complex zero finder}, Author = {M. J. Schaefer and T. Bubeck}, Journal = {Reliable Computing}, Year = {1995}, Number = {3}, Pages = {317--324}, Volume = {1} } @Article{Schaefer:2003:AEM, Title = {Accelerated Enclosure Methods for Ordinary Free Boundary Problems}, Author = {U. Schaefer}, Journal = {Reliable Computing}, Year = {2003}, Number = {5}, Pages = {391--403}, Volume = {9} } @Article{Schaefer:2002:TWE, Title = {Two Ways to Extend the {C}holesky Decomposition to Block Matrices with Interval Entries}, Author = {U. Schaefer}, Journal = {Reliable Computing}, Year = {2002}, Number = {1}, Pages = {1--20}, Volume = {8} } @Article{Schaefer:2001:FIG, Title = {The Feasibility of the Interval Gaussian Algorithm for Arrowhead Matrices}, Author = {U. Schaefer}, Journal = {Reliable Computing}, Year = {2001}, Number = {1}, Pages = {59--62}, Volume = {7} } @Article{Schnepper:1993:API, Title = {Application of a Parallel Interval {N}ewton/Generalized Bisection Algorithm to Equation-Based Chemical Process Flowsheeting}, Author = {C. A. Schnepper and M. A. Stadtherr}, Journal = {Interval Computations}, Year = {1993}, Number = {4}, Pages = {40--64} } @Article{Schnurr:2005:PSS, Title = {On the Proofs of Some Statements Concerning the Theorems of Kantorovich, Moore, and Miranda}, Author = {M. Schnurr}, Journal = {Reliable Computing}, Year = {2005}, Number = {1}, Pages = {77--85}, Volume = {11} } @Article{Schoen:2005:UZO, Title = {Using Zonotopes for Overestimation-Free Interval Least-Squares -- Some Geodetic Applications}, Author = {M. Schnurr}, Journal = {Reliable Computing}, Year = {2005}, Number = {2}, Pages = {137--155}, Volume = {11} } @Article{Schodl:2012:CNM, Title = {Continuity Notions for Multi--Valued Mappings with Possibly Disconnected Images}, Author = {Peter Schodl and Arnold Neumaier}, Journal = {Reliable Computing}, Year = {2012}, Month = {Mar}, Number = {1}, Pages = {84--101}, Volume = {16} } @Article{Schroecker:2006:GCD, Title = {Geometric Constructions with Discretized Random Variables}, Author = {H.-P. Schroecker and J. Wallner}, Journal = {Reliable Computing}, Year = {2006}, Number = {3}, Pages = {203--223}, Volume = {12} } @Article{Schulte:1996:VPI, Title = {Variable-precision, interval arithmetic coprocessors}, Author = {M. J. Schulte and E. E. Swartzlander, Jr.}, Journal = {Reliable Computing}, Year = {1996}, Number = {1}, Pages = {47--62}, Volume = {2} } @Article{Schulte:1995:SIH, Title = {A software interface and hardware design for variable-precision interval arithmetic}, Author = {M. J. Schulte and E. E. Swartzlander, Jr.}, Journal = {Reliable Computing}, Year = {1995}, Number = {3}, Pages = {325--342}, Volume = {1} } @Article{Schulte:1993:PHD, Title = {Parallel Hardware Designs for Correctly Rounded Elementary Functions}, Author = {M. J. Schulte and E. E. Swartzlander, Jr.}, Journal = {Interval Computations}, Year = {1993}, Number = {4}, Pages = {65--88} } @Article{Schulte:1999:IEG, Title = {The Interval-Enhanced {GNU} {F}ortran Compiler}, Author = {M. J. Schulte and V. Zelov and A. Akkas and J. C. Burley}, Journal = {Reliable Computing}, Year = {1999}, Number = {3}, Pages = {311--322}, Volume = {5} } @Article{Schwandt:2001:SAI, Title = {Synchronous and Asynchronous Interval {N}ewton-{S}chwarz Methods for a Class of Large Systems of Nonlinear Equations }, Author = {H. Schwandt}, Journal = {Reliable Computing}, Year = {2001}, Number = {4}, Pages = {281--306}, Volume = {7} } @Article{Schwandt:1994:SEI, Title = {Suboptimal Enclosures for the Interval {B}uneman Algorithm for Arbitrary Block Dimension}, Author = {H. Schwandt}, Journal = {Interval Computations}, Year = {1994}, Number = {1}, Pages = {51--90} } @Article{Senio:1992:SSS, Title = {Solving systems of special form nonlinear equations by means of some modifications of {R}unge type interval iterative method}, Author = {P. S. Senio and P. S. Vengersky}, Journal = {Interval Computations}, Year = {1992}, Number = {4}, Pages = {59--65} } @Article{Sharaya:2015:BIM, Title = {Boundary Intervals Method for Visualization of Polyhedral Solution Sets}, Author = {Irene A. Sharaya}, Journal = {Reliable Computing}, Year = {2015}, Month = {May}, Number = {4}, Pages = {435--467}, Volume = {19} } @Article{Sharaya:2005:UTS, Title = {On Unbounded Tolerable Solution Sets}, Author = {I. A. Sharaya}, Journal = {Reliable Computing}, Year = {2005}, Number = {5}, Pages = {425--432}, Volume = {11} } @Article{Sharaya:2001:MIE, Title = {On Maximal Inner Estimation of the Solution Sets of Linear Systems with Interval Parameters}, Author = {I. A. Sharaya}, Journal = {Reliable Computing}, Year = {2001}, Number = {5}, Pages = {409--424}, Volume = {7} } @Article{Sharaya:2011:TSS, Title = {Tolerable Solution Set for Interval Linear Systems with Constraints on Coefficients}, Author = {Irene A. Sharaya and Sergey P. Shary}, Journal = {Reliable Computing}, Year = {2011}, Month = {Jul}, Number = {4}, Pages = {345--357}, Volume = {15} } @Article{Shary:2015:OIS, Title = {Obituary: {Irene Sharaya} (1962--2015)}, Author = {Sergey P. Shary}, Journal = {Reliable Computing}, Year = {2015}, Month = {Mar}, Number = {1}, Pages = {113--114}, Volume = {20} } @Article{Shary:2011:NIL, Title = {On Nonnegative Interval Linear Systems and Their Solution}, Author = {Sergey P. Shary}, Journal = {Reliable Computing}, Year = {2011}, Month = {Jul}, Number = {4}, Pages = {358--369}, Volume = {15} } @Article{Shary:2002:NTS, Title = {A New Technique in Systems Analysis under Interval Uncertainty and Ambiguity}, Author = {S. P. Shary}, Journal = {Reliable Computing}, Year = {2002}, Number = {5}, Pages = {321--418}, Volume = {8} } @Article{Shary:2001:IGS, Title = {Interval {G}auss-{S}eidel Method for Generalized Solution Sets to Interval Linear Systems}, Author = {S. P. Shary}, Journal = {Reliable Computing}, Year = {2001}, Number = {2}, Pages = {141--155}, Volume = {7} } @Article{Shary:2001:SAI, Title = {A Surprising Approach in Interval Global Optimization}, Author = {S. P. Shary}, Journal = {Reliable Computing}, Year = {2001}, Number = {6}, Pages = {497--505}, Volume = {7} } @Article{Shary:1999:OEG, Title = {Outer Estimation of Generalized Solution Sets to Interval Linear System}, Author = {S. P. Shary}, Journal = {Reliable Computing}, Year = {1999}, Number = {3}, Pages = {323--335}, Volume = {5} } @Article{Shary:1997:AAO, Title = {Algebraic Approach in the ``Outer Problem'' for Interval Linear Equations}, Author = {S. P. Shary}, Journal = {Reliable Computing}, Year = {1997}, Number = {2}, Pages = {103--135}, Volume = {3} } @Article{Shary:1996:AAI, Title = {Algebraic approach to the interval linear static identification, tolerance, and control problems, or One more application of {K}aucher arithmetic}, Author = {S. P. Shary}, Journal = {Reliable Computing}, Year = {1996}, Number = {1}, Pages = {3--34}, Volume = {2} } @Article{Shary:1994:STP, Title = {Solving the Tolerance Problem for Interval Linear Systems}, Author = {S. P. Shary}, Journal = {Interval Computations}, Year = {1994}, Number = {2}, Pages = {6--26} } @Article{Shary:1992:CSS, Title = {On controlled solution set of interval algebraic systems}, Author = {S. P. Shary}, Journal = {Interval Computations}, Year = {1992}, Number = {4}, Pages = {66--75} } @Article{Shary:1992:NCA, Title = {A new class of algorithms for optimal solution of interval linear systems}, Author = {S. P. Shary}, Journal = {Interval Computations}, Year = {1992}, Number = {2}, Pages = {18--29} } @Article{Shary:1991:CLT, Title = {On compatibility of linear tolerance problem}, Author = {S. P. Shary}, Journal = {Interval Computations}, Year = {1991}, Number = {1}, Pages = {92--98} } @Article{Shary:1991:OSI, Title = {Optimal solution of the interval linear algebraic systems}, Author = {S. P. Shary}, Journal = {Interval Computations}, Year = {1991}, Number = {2}, Pages = {7--30} } @Article{Shashikhin:2001:RCU, Title = {Robust Control Using Interval Analysis}, Author = {V. N. Shashikhin}, Journal = {Reliable Computing}, Year = {2001}, Number = {3}, Pages = {219--230}, Volume = {7} } @Article{Shi:1996:IEI, Title = {Improving the efficiency index in enclosing a root of an equation}, Author = {Y. Shi}, Journal = {Reliable Computing}, Year = {1996}, Number = {4}, Pages = {357--372}, Volume = {2} } @Article{Shiriaev:1992:PPP, Title = {{PASCAL--XSC}. {A} portable programming system for scientific computations}, Author = {D. Shiriaev}, Journal = {Interval Computations}, Year = {1992}, Number = {4}, Pages = {76--82} } @Article{Shou:2006:RPP, Title = {Robust Plotting of Polar Algebraic Curves, Space Algebraic Curves, and Offsets of Planar Algebraic Curves}, Author = {H. Shou and J. Shen and D. Yoon}, Journal = {Reliable Computing}, Year = {2006}, Number = {4}, Pages = {323--335}, Volume = {12} } @Article{Simcik:1993:BBI, Title = {Boundary-Based Interval {N}ewton's Method}, Author = {L. Simcik and P. Linz}, Journal = {Interval Computations}, Year = {1993}, Number = {4}, Pages = {89--99} } @Article{Simoff:1992:IAR, Title = {Interval approximate reasoning for expert systems}, Author = {S. J. Simoff}, Journal = {Interval Computations}, Year = {1992}, Number = {4}, Pages = {83--87} } @Article{Sirisaengtaksin:1993:NNN, Title = {Neural Networks That Are Not Sensitive To The Imprecision of Hardware Neurons}, Author = {O. Sirisaengtaksin and V. Kreinovich}, Journal = {Interval Computations}, Year = {1993}, Number = {4}, Pages = {100--113} } @Article{Skalna:2006:MOI, Title = {A Method for Outer Interval Solution of Systems of Linear Equations Depending Linearly on Interval Parameters}, Author = {I. Skalna}, Journal = {Reliable Computing}, Year = {2006}, Number = {2}, Pages = {107--120}, Volume = {12} } @Article{Skybytsky:1992:CLD, Title = {Control of the linear dynamic plant with intervally given parameters from the guarantee condition of the required accuracy of the solution}, Author = {N. V. Skybytsky and T. Yuping}, Journal = {Interval Computations}, Year = {1992}, Number = {4}, Pages = {88--93} } @Article{Smagina:1992:GPA, Title = {General problem of the asymptotic steady-output tracking for plant with interval parameters}, Author = {E. M. Smagina}, Journal = {Interval Computations}, Year = {1992}, Number = {4}, Pages = {94--99} } @Article{Smagina:1997:NAM, Title = {A New Approach to the Modal Regulator Synthesis for Interval Plant with Scalar Input}, Author = {Y. M. Smagina}, Journal = {Reliable Computing}, Year = {1997}, Number = {4}, Pages = {401--410}, Volume = {3} } @Article{Smith:2007:RAE, Title = {Requirements Analysis for Engineering Computation: A Systematic Approach for Improving Reliability}, Author = {S. Smith and L. Lai and R. Khedri}, Journal = {Reliable Computing}, Year = {2007}, Number = {1}, Pages = {83--107}, Volume = {13} } @Article{Sokolova:2003:ASI, Title = {Asymptotic Stability of Interval Time-Delay Systems}, Author = {S. P. Sokolova and R. S. Ivlev}, Journal = {Reliable Computing}, Year = {2003}, Number = {4}, Pages = {303--313}, Volume = {9} } @Article{Solary:2013:FSE, Title = {Finding the Smallest Eigenvalue by Properties of Semidefinite Matrices}, Author = {Maryam Shams Solary}, Journal = {Reliable Computing}, Year = {2013}, Month = {Jun}, Number = {1}, Pages = {82--89}, Volume = {18} } @Article{Stahl:1997:ERT, Title = {Error Reduction of the Taylor Centered Form by Half and an Inner Estimation of the Range}, Author = {V. Stahl}, Journal = {Reliable Computing}, Year = {1997}, Number = {4}, Pages = {411--420}, Volume = {3} } @Article{Stipanovic:2000:JGS, Title = {{J}acobi and {G}auss-{S}eidel Iterations for Polytopic Systems: Convergence via Convex {M}-Matrices}, Author = {D. M. Stipanovic and D. D. Siljak }, Journal = {Reliable Computing}, Year = {2000}, Number = {2}, Pages = {123--137}, Volume = {6} } @Article{Storck:1993:VCN, Title = {Verified Calculation of the Nodes and Weights for {G}aussian Quadrature Formulas}, Author = {U. Storck}, Journal = {Interval Computations}, Year = {1993}, Number = {4}, Pages = {114--124} } @Article{Stoye:2007:BGL, Title = {Bounds on Generalized Linear Predictors with Incomplete Outcome Data}, Author = {J. Stoye}, Journal = {Reliable Computing}, Year = {2007}, Number = {3}, Pages = {293--302}, Volume = {13} } @Article{Strzebonski:1999:RPD, Title = {A Real Polynomial Decision Algorithm Using Arbitrary-Precision Floating Point Arithmetic}, Author = {A. Strzebonski}, Journal = {Reliable Computing}, Year = {1999}, Number = {3}, Pages = {337--346}, Volume = {5} } @Article{Sugihara:1996:NSB, Title = {Numerical solutions of {B}urgers' equation with a large {R}eynolds number}, Author = {M. Sugihara and S. Fujino}, Journal = {Reliable Computing}, Year = {1996}, Number = {2}, Pages = {173--180}, Volume = {2} } @Article{Sweidan:2001:TEC, Title = {On the Theory of Error Control Based on Moduli with Common Factors}, Author = {A. Sweidan and A. Jordan and A. A. Hiasat}, Journal = {Reliable Computing}, Year = {2001}, Number = {3}, Pages = {209--218}, Volume = {7} } @Article{Szulc:1996:RCC, Title = {Rank of convex combinations of matrices}, Author = {T. Szulc}, Journal = {Reliable Computing}, Year = {1996}, Number = {2}, Pages = {181--186}, Volume = {2} } @Article{Tapaswini:2014:NMA, Title = {New Midpoint--based Approach for the Solution of $n$--th Order Differential Equations}, Author = {Smita Tapaswini and S. Chakraverty}, Journal = {Reliable Computing}, Year = {2014}, Month = {Apr}, Number = {1}, Pages = {25--44}, Volume = {20} } @Article{Ten:1992:SOC, Title = {Synthesis of optimal control under interval uncertainty in models}, Author = {I. G. Ten}, Journal = {Interval Computations}, Year = {1992}, Number = {4}, Pages = {100--106} } @Article{Tischler:2011:SDP, Title = {Solving Decidability Problems with Interval Arithmetic}, Author = {German Tischler and J{\"{u}}rgen {Wolff von Gudenberg}}, Journal = {Reliable Computing}, Year = {2011}, Month = {Jul}, Number = {3}, Pages = {279--289}, Volume = {15} } @Article{Tonon:2007:SAC, Title = {A Search Algorithm for Calculating Validated Reliability Bounds}, Author = {F. Tonon}, Journal = {Reliable Computing}, Year = {2007}, Number = {2}, Pages = {195--209}, Volume = {13} } @Article{Tonon:2004:URS, Title = {On the Use of Random Set Theory to Bracket the Results of Monte Carlo Simulations}, Author = {F. Tonon}, Journal = {Reliable Computing}, Year = {2004}, Number = {2}, Pages = {107--137}, Volume = {10} } @Article{Torres:2004:EDI, Title = {Eliminating Duplicates under Interval and Fuzzy Uncertainty: An Asymptotically Optimal Algorithm and Its Geospatial Applications}, Author = {R. Torres and G. R. Keller and V. Kreinovich and L. Longpre and S. A. Starks}, Journal = {Reliable Computing}, Year = {2004}, Number = {5}, Pages = {401--422}, Volume = {10} } @Article{Toth:2005:EIC, Title = {Empirical Investigation of the Convergence Speed of Inclusion Functions in a Global Optimization Context}, Author = {B. Toth and T. Csendes}, Journal = {Reliable Computing}, Year = {2005}, Number = {4}, Pages = {253--273}, Volume = {11} } @Article{Traylor:1995:BSN, Title = {A bright side of {NP}-hardness of interval computations: interval heuristics applied to {NP}-problems}, Author = {B. Traylor and V. Kreinovich}, Journal = {Reliable Computing}, Year = {1995}, Number = {3}, Pages = {343--360}, Volume = {1} } @Article{Tucker:2006:PRB, Title = {Parameter Reconstruction for Biochemical Networks Using Interval Analysis}, Author = {W. Tucker and V. Moulton}, Journal = {Reliable Computing}, Year = {2006}, Number = {5}, Pages = {389--402}, Volume = {12} } @Article{Tupelly:2005:CEM, Title = {Checking If There Exists a Monotonic Function That Is Consistent with the Measurements: An Efficient Algorithm}, Author = {K. Tupelly and V. Kreinovich and K. Villaverde}, Journal = {Reliable Computing}, Year = {2005}, Number = {4}, Pages = {291--312}, Volume = {11} } @Article{Turksen:1993:IVF, Title = {Interval Valued Fuzzy Sets and Fuzzy Connectives}, Author = {I. B. Turksen}, Journal = {Interval Computations}, Year = {1993}, Number = {4}, Pages = {125--142} } @Article{Ullrich:1995:RLA, Title = {A reliable linear algebra library for transputer networks}, Author = {C. P. Ullrich and R. Reith}, Journal = {Reliable Computing}, Year = {1995}, Number = {2}, Pages = {173--188}, Volume = {1} } @Article{Utkin:2005:CSR, Title = {Computing System Reliability Given Interval-Valued Characteristics of the Components}, Author = {L. V. Utkin and I. O. Kozine}, Journal = {Reliable Computing}, Year = {2005}, Number = {1}, Pages = {19--34}, Volume = {11} } @Article{Emden:2011:FIA, Title = {From Interval Arithmetic to Interval Constraints}, Author = {M. H. {van Emden}}, Journal = {Reliable Computing}, Year = {2011}, Month = {Jun}, Number = {2}, Pages = {144--155}, Volume = {15} } @Article{Vehi:2000:ARP, Title = {Analysis of the Robustness of Predictive Controllers via Modal Intervals}, Author = {J. Vehi and J. Rodellar and M. Sainz and J. Armengol}, Journal = {Reliable Computing}, Year = {2000}, Number = {3}, Pages = {281--301}, Volume = {6} } @Article{Veliov:1993:CIU, Title = {Computation of Integrals of Uncertain Vector Functions}, Author = {V. M. Veliov}, Journal = {Interval Computations}, Year = {1993}, Number = {4}, Pages = {143--153} } @Article{Villa:1993:EEI, Title = {Estimating Errors of Indirect Measurement on Realistic Parallel Machines: Routings on 2-{D} and 3-{D} Meshes That are Nearly Optimal}, Author = {E. Villa and A. Bernat and V. Kreinovich}, Journal = {Interval Computations}, Year = {1993}, Number = {4}, Pages = {154--175} } @Article{Villaverde:1993:LTA, Title = {A Linear-Time Algorithm That Locates Local Extrema of a Function of One Variable From Interval Measurement Results}, Author = {K. Villaverde and V. Kreinovich}, Journal = {Interval Computations}, Year = {1993}, Number = {4}, Pages = {176--194} } @Article{Villaverde:2011:EVU, Title = {Estimating Variance under Interval and Fuzzy Uncertainty: {P}arallel Algorithms}, Author = {Karen Villaverde and Gang Xiang}, Journal = {Reliable Computing}, Year = {2011}, Month = {May}, Number = {1}, Pages = {60--68}, Volume = {15} } @Article{Voschchinin:1992:SQA, Title = {Some questions of application of interval mathematics in parameter estimation and decision making}, Author = {A. P. Voshchinin}, Journal = {Interval Computations}, Year = {1992}, Number = {4}, Pages = {107--115} } @Article{Vrahatis:1996:LCC, Title = {Locating, characterizing and computing the stationary points of a function}, Author = {M. N. Vrahatis and E. C. Triantafyllow}, Journal = {Reliable Computing}, Year = {1996}, Number = {2}, Pages = {187--194}, Volume = {2} } @Article{Wallner:2005:TGC, Title = {Tolerances in Geometric Constraint Problems}, Author = {J. Wallner and H.-P. Schroecker and S.-M. Hu}, Journal = {Reliable Computing}, Year = {2005}, Number = {3}, Pages = {235--251}, Volume = {11} } @Article{Wang:2012:NUF, Title = {A New Uncertainty--Bearing Floating--Point Arithmetic}, Author = {Chengpu Wang}, Journal = {Reliable Computing}, Year = {2012}, Month = {Dec}, Number = {1}, Pages = {308--361}, Volume = {16} } @Article{Wang:2000:CIC, Title = {Composite Interval Control Systems: Some Strong {K}haritonov-Like Properties}, Author = {L. Wang}, Journal = {Reliable Computing}, Year = {2000}, Number = {3}, Pages = {231--246}, Volume = {6} } @Article{Wang:2007:SIC, Title = {Solving Interval Constraints by Linearization in Computer-Aided Design}, Author = {Y. Wang and B. O. Nnaji}, Journal = {Reliable Computing}, Year = {2007}, Number = {2}, Pages = {211--244}, Volume = {13} } @Article{Watanabe:1999:NVM, Title = {A Numerical Verification Method of Solutions for the {N}avier-{S}tokes Equations}, Author = {Y. Watanabe and N. Yamamoto and M. T. Nakao }, Journal = {Reliable Computing}, Year = {1999}, Number = {3}, Pages = {347--357}, Volume = {5} } @Article{Weinhofer:1997:HCP, Title = {$H_\infty$-Control using Polynomial Matrices and Interval Arithmetic}, Author = {J. Weinhofer and W. Haas}, Journal = {Reliable Computing}, Year = {1997}, Number = {3}, Pages = {229--237}, Volume = {3} } @Article{Wolfe:2002:BPZ, Title = {Bounding Perturbations in Zeros of Nonlinear Systems}, Author = {M. A. Wolfe}, Journal = {Reliable Computing}, Year = {2002}, Number = {3}, Pages = {177--188}, Volume = {8} } @Article{Wolfe:2001:BSU, Title = {On Bounding Solutions of Underdetermined Systems}, Author = {M. A. Wolfe}, Journal = {Reliable Computing}, Year = {2001}, Number = {3}, Pages = {195--207}, Volume = {7} } @Article{Wolfe:2001:NUT, Title = {A Note on a Uniqueness Theorem for the Second-Derivative Test of {Q}i}, Author = {M. A. Wolfe}, Journal = {Reliable Computing}, Year = {2001}, Number = {1}, Pages = {49--52}, Volume = {7} } @Article{Wolfe:1999:DMP, Title = {On Discrete Minimax Problems in {R} Using Interval Arithmetic}, Author = {M. A. Wolfe}, Journal = {Reliable Computing}, Year = {1999}, Number = {4}, Pages = {371--383}, Volume = {5} } @Article{Wolfe:1998:SDT, Title = {On a Second Derivative Test due to {Q}i}, Author = {M. A. Wolfe}, Journal = {Reliable Computing}, Year = {1998}, Number = {3}, Pages = {223--234}, Volume = {4} } @Article{Wolfe:1995:IAB, Title = {An Interval Algorithm for Bounding the Ranges of Real-Valued Functions of One Real Variable}, Author = {M. A. Wolfe}, Journal = {Reliable Computing}, Year = {1995}, Number = {1}, Pages = {31--50}, Volume = {3} } @Article{Worden:2001:IMN, Title = {Interval Methods in Non-Destructive Testing of Material Structures}, Author = {K. Worden and R. Osegueda and C. Ferregut and S. Nazarian and D. L. George and M. J. George and V. Kreinovich and O. Kosheleva and S. Cabrera }, Journal = {Reliable Computing}, Year = {2001}, Number = {4}, Pages = {341--352}, Volume = {7} } @Article{Wu:1995:CSR, Title = {Computation of the stability radius of a {S}chur polynomial: an orthogonal projection approach}, Author = {Q.-H. Wu and M. Mansour}, Journal = {Reliable Computing}, Year = {1995}, Number = {4}, Pages = {421--430}, Volume = {1} } @Article{Xiang:2006:FAC, Title = {Fast Algorithm for Computing the Upper Endpoint of Sample Variance for Interval Data: Case of Sufficiently Accurate Measurements}, Author = {G. Xiang}, Journal = {Reliable Computing}, Year = {2006}, Number = {1}, Pages = {59--64}, Volume = {12} } @Article{Xiang:2007:CPV, Title = {Computing Population Variance and Entropy under Interval Uncertainty: Linear-Time Algorithms}, Author = {G. Xiang and M. Ceberio and V. Kreinovich}, Journal = {Reliable Computing}, Year = {2007}, Number = {6}, Pages = {467--488}, Volume = {13} } @Article{Xiao:2016:IPI, Title = {Interval--Based Parameter Identification for Structural Static Problems}, Author = {Naijia Xiao and Francesco Fedele and Rafi L. Muhanna}, Journal = {Reliable Computing}, Year = {2016}, Month = {Jul}, Number = {1}, Pages = {47--72}, Volume = {23} } @Article{Yakovlev:1993:ML, Title = {Multiaspectness and Localization}, Author = {A. G. Yakovlev}, Journal = {Interval Computations}, Year = {1993}, Number = {4}, Pages = {195--209} } @Article{Yakovlev:1992:CAP, Title = {Classification approach to programming of localizational (interval) computations}, Author = {A. G. Yakovlev}, Journal = {Interval Computations}, Year = {1992}, Number = {1}, Pages = {61--84} } @Article{Yakovlev:1991:ICS, Title = {Interval computations - subject of research and useful tool}, Author = {A. G. Yakovlev}, Journal = {Interval Computations}, Year = {1991}, Number = {1}, Pages = {27--43} } @Article{Yamamura:2003:FASP, Title = {Finding All Solution Sets of Piecewise-Trapezoidal Equations Described by Set-Valued Functions}, Author = {K. Yamamura}, Journal = {Reliable Computing}, Year = {2003}, Number = {3}, Pages = {241--250}, Volume = {9} } @Article{Yamamura:2000:FASN, Title = {Finding All Solutions of Nonlinear Equations Using Linear Combinations of Functions}, Author = {K. Yamamura}, Journal = {Reliable Computing}, Year = {2000}, Number = {2}, Pages = {105--113}, Volume = {6} } @Article{Yamamura:2016:FAS, Title = {Finding All Solution Sets of Piecewise--Linear Interval Equations Using Integer Programming}, Author = {Kiyotaka Yamamura and Suguru Ishiguro}, Journal = {Reliable Computing}, Year = {2016}, Month = {Jul}, Number = {1}, Pages = {73--96}, Volume = {23} } @Article{Yamanaka:2011:NVA, Title = {A Note on a Verified Automatic Integration Algorithm}, Author = {Naoya Yamanaka and Masahide Kashiwagi and Shin'ichi Oishi and Takeshi Ogita}, Journal = {Reliable Computing}, Year = {2011}, Month = {Jun}, Number = {2}, Pages = {156--167}, Volume = {15} } @Article{Zaffalon:2003:TBC, Title = {Tree-Based Credal Networks for Classification}, Author = {M. Zaffalon and E. Fagiuoli}, Journal = {Reliable Computing}, Year = {2003}, Number = {6}, Pages = {487--509}, Volume = {9} } @Article{Zakharov:1991:APA, Title = {Actual problems of applied mathematics. {A}ll-Union conference. {S}aratov, {M}ay 20-22, 1991. {A} brief report}, Author = {A. V. Zakharov}, Journal = {Interval Computations}, Year = {1991}, Number = {2}, Pages = {87--90} } @Article{Zelawski:1991:RNA, Title = {Rigorous Numerical Approach to Isolation in Dynamical Systems on the Example of the {K}uramoto-{S}ivashinsky Equation}, Author = {Marcin Zelawski}, Journal = {Reliable Computing}, Year = {1999}, Number = {2}, Pages = {113--129}, Volume = {5} } @Article{Zhenyu:1998:IEP, Title = {An Interval Entropy Penalty Method for Nonlinear Global Optimization}, Author = {H. Zhenyu}, Journal = {Reliable Computing}, Year = {1998}, Number = {1}, Pages = {15--25}, Volume = {4} } @Article{Zhilin:2005:FED, Title = {On Fitting Empirical Data under Interval Error}, Author = {S. I. Zhilin}, Journal = {Reliable Computing}, Year = {2005}, Number = {5}, Pages = {433--442}, Volume = {11} } @Article{Zimmer:2011:SMV, Title = {Sparse Matrices and Vectors in {C--XSC}}, Author = {Michael Zimmer and Walter Kr{\"{a}}mer and Werner Hofschuster}, Journal = {Reliable Computing}, Year = {2011}, Month = {Jan}, Number = {1}, Pages = {138--160}, Volume = {14} } @Article{Zyuzin:1992:EFD, Title = {The extension of the {F}rechet derivative concept in the interval-segment analysis}, Author = {V. S. Zyuzin}, Journal = {Interval Computations}, Year = {1992}, Number = {4}, Pages = {127--132} } @Article{Zyuzin:1992:MIS, Title = {On metrization of interval sets {$I(R),\ I(R^n)$}}, Author = {V. S. Zyuzin}, Journal = {Interval Computations}, Year = {1992}, Number = {2}, Pages = {39--50} } @Article{Zyuzin:1991:RBB, Title = {Review of the book: {H}. {B}auch, {K}.-{U}. {J}ahn, {D}. {O}elschlaegel, {H}. {S}uesse, and {V}. {W}iebigke `{I}nterval Mathematics (Theory and Application)'}, Author = {V. S. Zyuzin}, Journal = {Interval Computations}, Year = {1991}, Number = {1}, Pages = {105--107}, Notes = {{D}. {O}elschlaegel, {H}. {S}uesse, {V}. {W}iebigke {I}ntervallmathematik ({T}eorie und {A}nwendungen). - {L}eipzig, {BSB B. G. T}eubner {V}erlagsgesellschaft, 1987, 260 S. ({M}athematisch-{N}aturwissenschaftliche {B}ibliothek, {B}and 72))} } @article{Goldsztejn:2010:IAR, Author = {Alexandre Goldsztejn and Luc Jaulin}, Journal = {Reliable Computing}, Month = {Jun}, Number = {1}, Pages = {1--23}, Title = {Inner Approximation of the Range of Vector-Valued Functions}, Volume = {14}, Year = {2010}} @article{Miyajima:2010:FVA, Author = {Shinya Miyajima and Takeshi Ogita and Siegfried M. Rump and Shin'ichi Oishi}, Journal = {Reliable Computing}, Month = {Jun}, Number = {1}, Pages = {24--45}, Title = {Fast Verification for All Eigenpairs in Symmetric Positive Definite Generalized Eigenvalue Problems}, Volume = {14}, Year = {2010}} @article{Patre:2010:RSF, Author = {B. M. Patre and P. J. Deore}, Journal = {Reliable Computing}, Month = {Jun}, Number = {1}, Pages = {46--60}, Title = {Robust State Feedback for Interval Systems: {A}n Interval Analysis Approach}, Volume = {14}, Year = {2010}} @article{Garloff:2010:KLN, Author = {J{\"u}rgen Garloff}, Journal = {Reliable Computing}, Month = {Jun}, Number = {1}, Pages = {61--65}, Title = {{Karl L. E. Nickel} (1924 -- 2009)}, Volume = {14}, Year = {2010}} @article{Beelitz:2010:CCT, Author = {Thomas Beelitz and Bruno Lang and Peer Ueberholz and Paul Willems}, Journal = {Reliable Computing}, Month = {Jun}, Number = {1}, Pages = {66--77}, Title = {Closing the Case $t = 3$ for 3-{D} Spherical $t$-Designs Using a Result-Verifying Nonlinear Solver}, Volume = {14}, Year = {2010}} @article{Hladik:2010:SSC, Author = {Milan Hlad{\'{i}}k}, Journal = {Reliable Computing}, Month = {Jun}, Number = {1}, Pages = {78--87}, Title = {Solution Sets of Complex Linear Interval Systems of Equations}, Volume = {14}, Year = {2010}} @article{Meslem:2010:GPS, Author = {Nacim Meslem and Nacim Ramdani and Yves Candau}, Journal = {Reliable Computing}, Month = {Jun}, Number = {1}, Pages = {88--104}, Title = {Guaranteed Parameter Set Estimation for Monotone Dynamical Systems Using Hybrid Automata}, Volume = {14}, Year = {2010}} @article{Corsaro:2010:AAI, Author = {Stefania Corsaro and Marina Marino}, Journal = {Reliable Computing}, Month = {Jun}, Number = {1}, Pages = {105--116}, Title = {Archetypal Analysis of Interval Data}, Volume = {14}, Year = {2010}} @article{Ray:2010:NSS, Author = {Shashwati Ray and P. S. V. Nataraj}, Journal = {Reliable Computing}, Month = {Jun}, Number = {1}, Pages = {117--137}, Title = {A New Strategy for Selecting Subdivision Point in the {B}ernstein Approach to Polynomial Optimization}, Volume = {14}, Year = {2010}} @article{Zimmer:2011:SMV, Author = {Michael Zimmer and Walter Kr{\"{a}}mer and Werner Hofschuster}, Journal = {Reliable Computing}, Month = {Jan}, Number = {1}, Pages = {138--160}, Title = {Sparse Matrices and Vectors in {C--XSC}}, Volume = {14}, Year = {2011}} @article{Alt:2011:ASL, Author = {Ren{\'{e}} Alt and Jean-Luc Lamotte and Svetoslav Markov}, Journal = {Reliable Computing}, Month = {May}, Number = {1}, Pages = {1--12}, Title = {On the Accuracy of the Solution of Linear Problems on the {CELL} Processor}, Volume = {15}, Year = {2011}} @article{Argaez:2011:SOS, Author = {Miguel Arg{\'{a}}ez}, Journal = {Reliable Computing}, Month = {May}, Number = {1}, Pages = {13--25}, Title = {Solving Overdetermined Systems in $l_{p}$ Quasi-Norms}, Volume = {15}, Year = {2011}} @article{Blomquist:2011:SCC, Author = {Frithjof Blomquist}, Journal = {Reliable Computing}, Month = {May}, Number = {1}, Pages = {26--35}, Title = {Staggered Correction Computations with Enhanced Accuracy and Extremely Wide Exponent Range}, Volume = {15}, Year = {2011}} @article{Bohlender:2011:DAO, Author = {Gerd Bohlender and Ulrich Kulisch}, Journal = {Reliable Computing}, Month = {May}, Number = {1}, Pages = {36--42}, Title = {Definition of the Arithmetic Operations and Comparison Relations for an Interval Arithmetic}, Volume = {15}, Year = {2011}} @article{Cheu:2011:TPO, Author = {Darrell Cheu and Luc Longpr{\'{e}}}, Journal = {Reliable Computing}, Month = {May}, Number = {1}, Pages = {43--46}, Title = {Towards the Possibility of Objective Interval Uncertainty in Physics}, Volume = {15}, Year = {2011}} @article{Goldsztejn:2011:CCP, Author = {Alexandre Goldsztejn and Yahia Lebbah and Claude Michel and Michel Rueher}, Journal = {Reliable Computing}, Month = {May}, Number = {1}, Pages = {47--59}, Title = {Capabilities of Constraint Programming in Safe Global Optimization}, Volume = {15}, Year = {2011}} @article{Villaverde:2011:EVU, Author = {Karen Villaverde and Gang Xiang}, Journal = {Reliable Computing}, Month = {May}, Number = {1}, Pages = {60--68}, Title = {Estimating Variance under Interval and Fuzzy Uncertainty: {P}arallel Algorithms}, Volume = {15}, Year = {2011}} @article{Hattangady:2011:BFP, Author = {Sandeep Hattangady and William Edmonson and Winser Alexander}, Journal = {Reliable Computing}, Month = {Jun}, Number = {2}, Pages = {69--80}, Title = {Block Floating Point Interval {ALU} for Digital Signal Processing}, Volume = {15}, Year = {2011}} @article{Petkovic:2011:CAI, Author = {Ivan Petkovi{\'{c}}}, Journal = {Reliable Computing}, Month = {Jun}, Number = {2}, Pages = {81--90}, Title = {Computational Aspects of the Implementation of Disk Inversions}, Volume = {15}, Year = {2011}} @article{Petkovic:2011:HOM, Author = {Miodrag S. Petkovi{\'{c}} and Du\v{s}an M. Milo{\v{s}}evi{\'{c}}}, Journal = {Reliable Computing}, Month = {Jun}, Number = {2}, Pages = {91--108}, Title = {Higher Order Methods for the Inclusion of Multiple Zeros of Polynomials}, Volume = {15}, Year = {2011}} @article{Nataraj:2011:INM, Author = {P. S. V. Nataraj and M. Arounassalame}, Journal = {Reliable Computing}, Month = {Jun}, Number = {2}, Pages = {109--119}, Title = {An Interval Newton Method Based on the {B}ernstein Form for Bounding the Zeros of Polynomial Systems}, Volume = {15}, Year = {2011}} @article{Diep:2011:SCS, Author = {Nguyen Hong Diep and Nathalie Revol}, Journal = {Reliable Computing}, Month = {Jun}, Number = {2}, Pages = {120--131}, Title = {Solving and Certifying the Solution of a Linear System}, Volume = {15}, Year = {2011}} @article{Pownuk:2011:AOP, Author = {Andrzej Pownuk and Naveen Kumar Goud Ramunigari}, Journal = {Reliable Computing}, Month = {Jun}, Number = {2}, Pages = {132--143}, Title = {Application of Order-Preserving Functions to the Modeling of Computational Mechanics Problems with Uncertainty}, Volume = {15}, Year = {2011}} @article{Emden:2011:FIA, Author = {M. H. {van Emden}}, Journal = {Reliable Computing}, Month = {Jun}, Number = {2}, Pages = {144--155}, Title = {From Interval Arithmetic to Interval Constraints}, Volume = {15}, Year = {2011}} @article{Yamanaka:2011:NVA, Author = {Naoya Yamanaka and Masahide Kashiwagi and Shin'ichi Oishi and Takeshi Ogita}, Journal = {Reliable Computing}, Month = {Jun}, Number = {2}, Pages = {156--167}, Title = {A Note on a Verified Automatic Integration Algorithm}, Volume = {15}, Year = {2011}} @article{Enszer:2011:VSP, Author = {Joshua A. Enszer and Mark A. Stadtherr}, Journal = {Reliable Computing}, Month = {Jul}, Number = {3}, Pages = {168--178}, Title = {Verified Solution and Propagation of Uncertainty in Physiological Models}, Volume = {15}, Year = {2011}} @article{Kempken:2011:VFM, Author = {Sebastian Kempken and Wolfram Luther}, Journal = {Reliable Computing}, Month = {Jul}, Number = {3}, Pages = {179--192}, Title = {Verifed Factorization Methods for {SMP/G/1} Queueing Systems and their Interplay in an Integrated Problem-Solving Environment}, Volume = {15}, Year = {2011}} @article{Kolberg:2011:EPS, Author = {Mariana Kolberg and Walter Kr{\"{a}}mer and Michael Zimmer}, Journal = {Reliable Computing}, Month = {Jul}, Number = {3}, Pages = {193--206}, Title = {Efficient Parallel Solvers for Large Dense Systems of Linear Interval Equations}, Volume = {15}, Year = {2011}} @article{Kubica:2011:IMS, Author = {Bart{\l{}}omiej Jacek Kubica}, Journal = {Reliable Computing}, Month = {Jul}, Number = {3}, Pages = {207--217}, Title = {Interval Methods for Solving Underdetermined Nonlinear Systems}, Volume = {15}, Year = {2011}} @article{Magoc:2011:UPC, Author = {Tanja Mago{\v{c}} and Martine Ceberio and Francois Modave}, Journal = {Reliable Computing}, Month = {Jul}, Number = {3}, Pages = {218--229}, Title = {Using Preference Constraints to Solve Multi-Criteria Decision Making Problems}, Volume = {15}, Year = {2011}} @article{Argaez:2011:HAG, Author = {Miguel Arg{\'{a}}ez and Leticia Vel{\'{a}}zquez and Carlos Quintero and Hector Klie and Mary Wheeler}, Journal = {Reliable Computing}, Month = {Jul}, Number = {3}, Pages = {230--241}, Title = {A Hybrid Algorithm for Global Optimization Problems}, Volume = {15}, Year = {2011}} @article{Roy:2011:GOS, Author = {Julie Roy and R. Baker Kearfott}, Journal = {Reliable Computing}, Month = {Jul}, Number = {3}, Pages = {242--250}, Title = {Global Optimization and Singular Nonlinear Programs: {N}ew Techniques}, Volume = {15}, Year = {2011}} @article{Nataraj:2011:ETM, Author = {P. S. V. Nataraj and Shanta Sondur}, Journal = {Reliable Computing}, Month = {Jul}, Number = {3}, Pages = {251--278}, Title = {The Extrapolated {T}aylor Model}, Volume = {15}, Year = {2011}} @article{Tischler:2011:SDP, Author = {German Tischler and J{\"{u}}rgen {Wolff von Gudenberg}}, Journal = {Reliable Computing}, Month = {Jul}, Number = {3}, Pages = {279--289}, Title = {Solving Decidability Problems with Interval Arithmetic}, Volume = {15}, Year = {2011}} @article{Kapitanski:2011:DRC, Author = {Lev Kapitanski and Sanja {\v{Z}}ivanovi{\v{c}}}, Journal = {Reliable Computing}, Month = {Jul}, Number = {4}, Pages = {290--299}, Title = {Dynamics with a Range of Choice}, Volume = {15}, Year = {2011}} @article{Magoc:2011:AFM, Author = {Tanja Mago{\v{c}} and Xiaojing Wang and Francois Modave and Martine Ceberio}, Journal = {Reliable Computing}, Month = {Jul}, Number = {4}, Pages = {300--311}, Title = {Applications of Fuzzy Measures and Intervals in Finance}, Volume = {15}, Year = {2011}} @article{Nehmeier:2011:FET, Author = {M. Nehmeier and J{\"{u}}rgen {Wolff von Gudenberg}}, Journal = {Reliable Computing}, Month = {Jul}, Number = {4}, Pages = {312--320}, Title = {filib++ Expression Templates and the Coming Interval Standard}, Volume = {15}, Year = {2011}} @article{Rauh:2011:DRO, Author = {Andreas Rauh and Ekaterina Auer and Mareile Freihold and Eberhard P. Hofer and Harald Aschemann}, Journal = {Reliable Computing}, Month = {Jul}, Number = {4}, Pages = {321--332}, Title = {Detection and Reduction of Overestimation in Guaranteed Simulations of {H}amiltonian Systems}, Volume = {15}, Year = {2011}} @article{Rauh:2011:ROC, Author = {Andreas Rauh and Johanna Minisini and Eberhard P. Hofer and Harald Aschemann}, Journal = {Reliable Computing}, Month = {Jul}, Number = {4}, Pages = {333--344}, Title = {Robust and Optimal Control of Uncertain Dynamical Systems with State-Dependent Switchings Using Interval Arithmetic}, Volume = {15}, Year = {2011}} @article{Sharaya:2011:TSS, Author = {Irene A. Sharaya and Sergey P. Shary}, Journal = {Reliable Computing}, Month = {Jul}, Number = {4}, Pages = {345--357}, Title = {Tolerable Solution Set for Interval Linear Systems with Constraints on Coefficients}, Volume = {15}, Year = {2011}} @article{Shary:2011:NIL, Author = {Sergey P. Shary}, Journal = {Reliable Computing}, Month = {Jul}, Number = {4}, Pages = {358--369}, Title = {On Nonnegative Interval Linear Systems and Their Solution}, Volume = {15}, Year = {2011}} @article{Rauh:2011:VSO, Author = {Andreas Rauh and Ekaterina Auer}, Journal = {Reliable Computing}, Month = {Jul}, Number = {4}, Pages = {370--381}, Title = {Verified Simulation of {ODEs} and {DAEs} in {ValEncIA-IVP}}, Volume = {15}, Year = {2011}} @article{Kolev:2011:MDR, Author = {Lubomir V. Kolev}, Journal = {Reliable Computing}, Month = {Jul}, Number = {1}, Pages = {1--26}, Title = {A Method for Determining the Regularity Radius of Interval Matrices}, Volume = {16}, Year = {2011}} @article{Hladik:2011:ESM, Author = {Milan Hlad{\'{i}}k and Luc Jaulin}, Journal = {Reliable Computing}, Month = {Oct}, Number = {1}, Pages = {27--37}, Title = {An Eigenvalue Symmetric Matrix Contractor}, Volume = {16}, Year = {2011}} @article{Karmakar:2012:CSD, Author = {Samiran Karmakar and A. K. Bhunia}, Journal = {Reliable Computing}, Month = {Jan}, Number = {1}, Pages = {38--72}, Title = {A Comparative Study of Different Order Relations of Intervals}, Volume = {16}, Year = {2012}} @article{Just:2012:SSE, Author = {Elke Just and Bruno Lang}, Journal = {Reliable Computing}, Month = {Mar}, Number = {1}, Pages = {73--83}, Title = {A Success--Guided Selection of Expanded Systems for Result--Verifying Nonlinear Solvers}, Volume = {16}, Year = {2012}} @article{Schodl:2012:CNM, Author = {Peter Schodl and Arnold Neumaier}, Journal = {Reliable Computing}, Month = {Mar}, Number = {1}, Pages = {84--101}, Title = {Continuity Notions for Multi--Valued Mappings with Possibly Disconnected Images}, Volume = {16}, Year = {2012}} @article{Miyajima:2012:CEE, Author = {Shinya Miyajima}, Journal = {Reliable Computing}, Month = {Apr}, Number = {1}, Pages = {102--106}, Title = {Componentwise Error Estimates for Solutions Obtained by Stationary Iterative Methods}, Volume = {16}, Year = {2012}} @article{Miyajima:2012:RBT, Author = {Shinya Miyajima}, Journal = {Reliable Computing}, Month = {Apr}, Number = {1}, Pages = {107--113}, Title = {The Relation between Two Types of Error Bounds for Computed Matrix Eigenvalues}, Volume = {16}, Year = {2012}} @article{Kiel:2012:YYA, Author = {Stefan Kiel}, Journal = {Reliable Computing}, Month = {Sep}, Number = {1}, Pages = {114--129}, Title = {{YalAA}: {Y}et Another Library for Affine Arithmetic}, Volume = {16}, Year = {2012}} @article{Goldsztejn:2012:MIO, Author = {Alexandre Goldsztejn}, Journal = {Reliable Computing}, Month = {Oct}, Number = {1}, Pages = {130--183}, Title = {Modal Intervals Revisited, Part 1: {A} Generalized Interval Natural Extension}, Volume = {16}, Year = {2012}} @article{Goldsztejn:2012:MIT, Author = {Alexandre Goldsztejn}, Journal = {Reliable Computing}, Month = {Oct}, Number = {1}, Pages = {184--209}, Title = {Modal Intervals Revisited, Part 2: {A} Generalized Interval Mean Value Extension}, Volume = {16}, Year = {2012}} @article{Mayer:2012:EMR, Author = {G{\"{u}}nter Mayer}, Journal = {Reliable Computing}, Month = {Oct}, Number = {1}, Pages = {210--224}, Title = {On an Expression for the Midpoint and the Radius of the Product of Two Intervals}, Volume = {16}, Year = {2012}} @article{Milosevic:2012:OMI, Author = {Mimica R. Milo\v{s}evi{\'{c}} and Miodrag S. Petkovi{\'{c}}}, Journal = {Reliable Computing}, Month = {Oct}, Number = {1}, Pages = {225--238}, Title = {Ostrowski--Like Method for the Inclusion of a Single Complex Polynomial Zero}, Volume = {16}, Year = {2012}} @article{Herrero:2012:EIS, Author = {Pau Herrero and Pantelis Georgiou and Christofer Toumazou and Beno{\^{i}}t Delaunay and Luc Jaulin}, Journal = {Reliable Computing}, Month = {Oct}, Number = {1}, Pages = {239--251}, Title = {An Efficient Implementation of the {SIVIA} Algorithm in a High--Level Numerical Programming Language}, Volume = {16}, Year = {2012}} @article{Harlow:2012:MRP, Author = {Jennifer Harlow and Raazesh Sainudiin and Warwick Tucker}, Journal = {Reliable Computing}, Month = {Nov}, Number = {1}, Pages = {252--282}, Title = {Mapped Regular Pavings}, Volume = {16}, Year = {2012}} @article{Weerdt:2012:PIF, Author = {E. {de Weerdt} and E. {van Kampen} and Q. P. Chu and J. A. Mulder}, Journal = {Reliable Computing}, Month = {Nov}, Number = {1}, Pages = {283--307}, Title = {Polynomial Inclusion Functions}, Volume = {16}, Year = {2012}} @article{Wang:2012:NUF, Author = {Chengpu Wang}, Journal = {Reliable Computing}, Number = {1}, Month = {Dec}, Pages = {308--361}, Title = {A New Uncertainty--Bearing Floating--Point Arithmetic}, Volume = {16}, Year = {2012}} @article{Delgado:2012:OBR, Author = {Jorge Delgado and Juan Manuel Pe{\~{n}}a}, Journal = {Reliable Computing}, Month = {Dec}, Number = {1}, Pages = {1--10}, Title = {Optimality of {B}ernstein Representations for Computational Purposes}, Volume = {17}, Year = {2012}} @article{Leroy:2012:CUS, Author = {Richard Leroy}, Journal = {Reliable Computing}, Month = {Dec}, Number = {1}, Pages = {11--21}, Title = {Convergence under Subdivision and Complexity of Polynomial Minimization in the Simplicial {B}ernstein Basis}, Volume = {17}, Year = {2012}} @article{Michelucci:2012:CBC, Author = {Dominique Michelucci and Sebti Foufou and Arnaud Kubicki}, Journal = {Reliable Computing}, Month = {Dec}, Number = {1}, Pages = {22-- 33}, Title = {On the Complexity of the {B}ernstein Combinatorial Problem}, Volume = {17}, Year = {2012}} @article{Narkawicz:2012:BRR, Author = {Anthony Narkawicz and J{\"{u}}rgen Garloff and Andrew P. Smith and C{\'{e}}sar A. Mu{\~{n}}oz}, Journal = {Reliable Computing}, Month = {Dec}, Number = {1}, Pages = {34--39}, Title = {Bounding the Range of a Rational Function over a Box}, Volume = {17}, Year = {2012}} @article{Ray:2012:MME, Author = {Shashwati Ray and P. S. V. Nataraj}, Journal = {Reliable Computing}, Month = {Dec}, Number = {1}, Pages = {40--71}, Title = {A Matrix Method for Efficient Computation of {B}ernstein Coefficients}, Volume = {17}, Year = {2012}} @article{Bela:2012:RRA, Author = {Szilvia B{\'{e}}la and Bert J{\"{u}}ttler}, Journal = {Reliable Computing}, Month = {Dec}, Number = {2}, Pages = {72--96}, Title = {Real Root Approximation Using Fat Spheres}, Volume = {17}, Year = {2012}} @article{Crespo:2012:UFT, Author = {Luis G. Crespo and Daniel P. Giesy and Sean P. Kenny}, Journal = {Reliable Computing}, Month = {Dec}, Number = {2}, Pages = {97--127}, Title = {A Unifying Framework to Uncertainty Quantification of Polynomial Systems Subject to Aleatory and Epistemic Uncertainty}, Volume = {17}, Year = {2012}} @article{Dang:2012:RAP, Author = {Thao Dang and Romain Testylier}, Journal = {Reliable Computing}, Month = {Dec}, Number = {2}, Pages = {128--152}, Title = {Reachability Analysis for Polynomial Dynamical Systems Using the {B}ernstein Expansion}, Volume = {17}, Year = {2012}} @article{Visser:2012:INA, Author = {Coen C. {de Visser} and Eric-Jan {van Kampen} and Q. Ping Chu and J. A. Mulder}, Journal = {Reliable Computing}, Month = {Dec}, Number = {2}, Pages = {153--191}, Title = {Intersplines: {A} New Approach to Globally Optimal Multivariate Splines Using Interval Analysis}, Volume = {17}, Year = {2012}} @article{Foufou:2012:BBA, Author = {Sebti Foufou and Dominique Michelucci}, Journal = {Reliable Computing}, Month = {Dec}, Number = {2}, Pages = {192--208}, Title = {The {B}ernstein Basis and its Applications in Solving Geometric Constraint Systems}, Volume = {17}, Year = {2012}} @article{Narkawicz:2012:FVC, Author = {Anthony Narkawicz and C{\'{e}}sar A. Mu{\~{n}}oz}, Journal = {Reliable Computing}, Month = {Dec}, Number = {2}, Pages = {209--237}, Title = {Formal Verification of Conflict Detection Algorithms for Arbitrary Trajectories}, Volume = {17}, Year = {2012}} @article{Michalak:2013:IIP, Author = {Marcin Michalak and Vladik Kreinovich}, Journal = {Reliable Computing}, Month = {Jan}, Number = {1}, Pages = {1--8}, Title = {Is it Possible to Have a Feasible Enclosure--Computing Method Which Is Independent of the Equivalent Form?}, Volume = {18}, Year = {2013}} @article{Miyajima:2013:FEM, Author = {Shinya Miyajima}, Journal = {Reliable Computing}, Month = {Jan}, Number = {1}, Pages = {9--14}, Title = {Fast Enclosure of Matrix Polynomials}, Volume = {18}, Year = {2013}} @article{Sainudiin:2013:ATU, Author = {Raazesh Sainudiin and Thomas York}, Journal = {Reliable Computing}, Month = {Apr}, Number = {1}, Pages = {15--54}, Title = {An Auto--Validating, Trans--Dimensional, Universal Rejection Sampler for Locally {L}ipschitz Arithmetical Expressions}, Volume = {18}, Year = {2013}} @article{Jiang:2013:AVF, Author = {Hao Jiang and Housen Li and Lizhi Cheng and Roberto Barrio and Canbin Hu and Xiangke Liao}, Journal = {Reliable Computing}, Month = {May}, Number = {1}, Pages = {55--72}, Title = {Accurate, Validated and Fast Evaluation of {B}{\'{e}}zier Tensor Product Surfaces}, Volume = {18}, Year = {2013}} @article{Erascu:2013:SOQ, Author = {M{\={a}}d{\={a}}lina Era{\c{s}}cu and Hoon Hong}, Journal = {Reliable Computing}, Month = {May}, Number = {1}, Pages = {73--81}, Title = {The {S}ecant--{N}ewton Map is Optimal Among Contracting Quadratic Maps for Square Root Computation}, Volume = {18}, Year = {2013}} @article{Solary:2013:FSE, Author = {Maryam Shams Solary}, Journal = {Reliable Computing}, Month = {Jun}, Number = {1}, Pages = {82--89}, Title = {Finding the Smallest Eigenvalue by Properties of Semidefinite Matrices}, Volume = {18}, Year = {2013}} @article{Pownuk:2013:CMI, Author = {Andrzej Pownuk and Luc Longpr{\'e} and Vladik Kreinovich}, Journal = {Reliable Computing}, Month = {Jul}, Number = {1}, Pages = {90--96}, Title = {Checking Monotonicity is {NP}--Hard Even for Cubic Polynomials}, Volume = {18}, Year = {2013}} @article{Sainudiin:2013:RES, Author = {Raazesh Sainudiin and Thomas Steinke}, Journal = {Reliable Computing}, Month = {Sep}, Number = {1}, Pages = {97--116}, Title = {A Rigorous Extension of the {S}ch{\"o}nhage--{S}trassen Integer Multiplication Algorithm Using Complex Interval Arithmetic}, Volume = {18}, Year = {2013}} @article{Goubault:2013:GIA, Author = {Olivier Mullier and {\'E}ric Goubault and Michel Kieffer and Sylvie Putot}, Journal = {Reliable Computing}, Month = {Nov}, Number = {1}, Pages = {117--143}, Title = {General Inner Approximation of Vector--valued Functions}, Volume = {18}, Year = {2013}} @article{Hashemi:2013:NIM, Author = {Benham Hashemi and Hanieh Tavakolipour}, Journal = {Reliable Computing}, Month = {Nov}, Number = {1}, Pages = {144--146}, Title = {A Non--Induced Interval Matrix Norm}, Volume = {18}, Year = {2013}} @article{Saraev:2013:IPM, Author = {Pavel V. Saraev}, Journal = {Reliable Computing}, Month = {Dec}, Number = {1}, Pages = {147--156}, Title = {Interval Pseudo--Inverse Matrices and Interval {G}reville Algorithm}, Volume = {18}, Year = {2013}} @article{Gatilov:2013:EAS, Author = {Stepan Yu. Gatilov}, Journal = {Reliable Computing}, Month = {Aug}, Number = {1}, Pages = {1--25}, Title = {Efficient Angle Summation Algorithm for Point Inclusion Test and Its Robustness}, Volume = {19}, Year = {2013}} @article{Kostousova:2013:BUP, Author = {Elena K. Kostousova}, Journal = {Reliable Computing}, Month = {Nov}, Number = {1}, Pages = {26--44}, Title = {On Boundedness and Unboundedness of Polyhedral Estimates for Reachable Sets of Linear Differential Systems}, Volume = {19}, Year = {2013}} @article{Okayama:2013:EEE, Author = {Tomoaki Okayama}, Journal = {Reliable Computing}, Month = {Nov}, Number = {1}, Pages = {45--65}, Title = {Error Estimates with Explicit Constants for Sinc Quadrature and Sinc Indefinite Integration over Infinite Intervals}, Volume = {19}, Year = {2013}} @article{Rauh:2013:EET, Author = {Andreas Rauh and Ramona Westphal and Harald Aschemann and Ekaterina Auer}, Journal = {Reliable Computing}, Month = {Nov}, Number = {1}, Pages = {66--90}, Title = {Exponential Enclosure Techniques for the Computation of Guaranteed State Enclosures in {ValEncIA}--{IVP}}, Volume = {19}, Year = {2013}} @article{Revol:2013:PII, Author = {Nathalie Revol and Philippe Th{\'e}veny}, Journal = {Reliable Computing}, Month = {Nov}, Number = {1}, Pages = {91--106}, Title = {Parallel Implementation of Interval Matrix Multiplication}, Volume = {19}, Year = {2013}} @article{Prolubnikov:2013:IAT, Author = {Alexander V. Prolubnikov}, Journal = {Reliable Computing}, Month = {Nov}, Number = {1}, Pages = {107--119}, Title = {An Interval Approach to Pattern Recognition of Numerical Matrices}, Volume = {19}, Year = {2013}} @article{Labutin:2013:ASA, Author = {Ilya B. Labutin and Irina V. Surodina}, Journal = {Reliable Computing}, Month = {Dec}, Number = {1}, Pages = {120--126}, Title = {Algorithm for Sparse Approximate Inverse Preconditioners in the Conjugate Gradient Method}, Volume = {19}, Year = {2013}} @article{Minamihata:2013:FVS, Author = {A. Minamihata and K. Sekine and T. Ogita and S. Oishi}, Journal = {Reliable Computing}, Month = {Dec}, Number = {2}, Pages = {127--141}, Title = {Fast Verified Solutions of Sparse Linear Systems with {H}--matrices}, Volume = {19}, Year = {2013}} @article{Horacek:2013:CEO, Author = {J. Hor{\'a}{\v{c}}ek and M. Hlad{\'\i}k}, Journal = {Reliable Computing}, Month = {Nov}, Number = {2}, Pages = {142--155}, Title = {Computing Enclosures of Overdetermined Interval Linear Systems}, Volume = {19}, Year = {2013}} @article{Auer:2013:UVM, Author = {Ekaterina Auer and Stefan Kiel}, Journal = {Reliable Computing}, Month = {Dec}, Number = {2}, Pages = {156--175}, Title = {Uses of Verified Methods for Solving Non--Smooth Initial Value Problems}, Volume = {19}, Year = {2013}} @article{Lyudvin:2013:TIP, Author = {Dmitri Yu. Lyudvin and Sergey P. Shary}, Journal = {Reliable Computing}, Month = {Dec}, Number = {2}, Pages = {176--196}, Title = {Testing Implementations of {PPS}--methods for Interval Linear Systems}, Volume = {19}, Year = {2013}} @article{Kumkov:2013:IAT, Author = {Sergey I. Kumkov and Yuliya V. Mikushina}, Journal = {Reliable Computing}, Month = {Nov}, Number = {2}, Pages = {197--214}, Title = {Interval Approach to Identification of Catalytic Process Parameters}, Volume = {19}, Year = {2013}} @article{Panyukov:2013:CBP, Author = {Anatoly V. Panyukov and Valentin A. Golodov}, Journal = {Reliable Computing}, Month = {Dec}, Number = {2}, Pages = {215--228}, Title = {Computing Best Possible Pseudo--Solutions to Interval Linear Systems of Equations}, Volume = {19}, Year = {2013}} @article{Nadezhin:2014:JL, Author = {Dmitry Yu. Nadezhin and Sergei I. Zhilin}, Journal = {Reliable Computing}, Month = {Jan}, Number = {3}, Pages = {229--247}, Title = {{JI}nterval Library: {P}rinciples, Development, and Perspectives}, Volume = {19}, Year = {2014}} @article{Pushkarev:2013:MSD, Author = {Maxim I. Pushkarev and Sergey A. Gaivoronsky}, Journal = {Reliable Computing}, Month = {Dec}, Number = {3}, Pages = {248--260}, Title = {Maximizing Stability Degree of Control Systems under Interval Uncertainty Using a Coefficient Method}, Volume = {19}, Year = {2013}} @article{Jaulin:2014:OAA, Author = {Luc Jaulin}, Journal = {Reliable Computing}, Month = {Apr}, Number = {3}, Pages = {261--273}, Title = {Outer Approximation of Attractors Using an Interval Quantization}, Volume = {19}, Year = {2014}} @article{Dobronets:2014:NPA, Author = {Boris S. Dobronets and Olga A. Popova}, Journal = {Reliable Computing}, Month = {Apr}, Number = {3}, Pages = {274--289}, Title = {Numerical Probabilistic Analysis under Aleatory and Epistemic Uncertainty}, Volume = {19}, Year = {2014}} @article{Lakeyev:2014:UGS, Author = {Anatoly V. Lakeyev}, Journal = {Reliable Computing}, Month = {Apr}, Number = {3}, Pages = {290--301}, Title = {On Unboundedness of Generalized Solution Sets for Interval Linear Systems}, Volume = {19}, Year = {2014}} @article{Kiel:2014:ETV, Author = {Stefan Kiel and Ekaterina Auer and Andreas Rauh}, Journal = {Reliable Computing}, Month = {May}, Number = {3}, Pages = {302--317}, Title = {An Environment for Testing, Verification and Validation of Dynamical Models in the Context of Solid Oxide Fuel Cells}, Volume = {19}, Year = {2014}} @article{Savchenko:2014:CPA, Author = {Alexander Savchenko}, Journal = {Reliable Computing}, Month = {Apr}, Number = {3}, Pages = {318--329}, Title = {Computation of Potential and Attraction Force of an Ellipsoid}, Volume = {19}, Year = {2014}} @article{Rauh:2014:NVE, Author = {Andreas Rauh and Luise Senkel and Thomas D{\"o}vtschel and Harald Aschemann and Ekaterina Auer}, Journal = {Reliable Computing}, Month = {May}, Number = {4}, Pages = {330--350}, Title = {Numerical Verification and Experimental Validation of Sliding Mode Control Design for Uncertain Thermal {SOFC} Models}, Volume = {19}, Year = {2014}} @article{Dombrovskii:2014:MPC, Author = {Vladimir V. Dombrovskii and Elena V. Chausova}, Journal = {Reliable Computing}, Month = {Jun}, Number = {4}, Pages = {351--360}, Title = {Model Predictive Control for Linear Systems with Interval and Stochastic Uncertainties}, Volume = {19}, Year = {2014}} @article{Rauh:2014:IMS, Author = {Andreas Rauh and Luise Senkel and Julia Kersten and Harald Aschemann}, Journal = {Reliable Computing}, Month = {Jun}, Number = {4}, Pages = {361--384}, Title = {Interval Methods for Sensitivity--Based Model--Predictive Control of Solid Oxide Fuel Cell Systems}, Volume = {19}, Year = {2014}} @article{Kubica:2014:ERU, Author = {Bart{\l{}}omiej Jacek Kubica}, Journal = {Reliable Computing}, Month = {Jun}, Number = {4}, Pages = {385--397}, Title = {Excluding Regions Using Sobol Sequences in an Interval Branch--and--Prune Method for Nonlinear Systems}, Volume = {19}, Year = {2014}} @article{Montan:2014:EMM, Author = {Sethy Montan and Christophe Denis and Jean-Marie Chesneaux and Jean-Luc Lamotte}, Journal = {Reliable Computing}, Month = {Nov}, Number = {4}, Pages = {398--416}, Title = {Efficient Matrix Multiplication Based on Discrete Stochastic Arithmetic}, Volume = {19}, Year = {2014}} @article{Panyukov:2014:SAA, Author = {Anatoly V. Panyukov}, Journal = {Reliable Computing}, Month = {Nov}, Number = {4}, Pages = {417--434}, Title = {Scalability of Algorithms for Arithmetic Operations in Radix Notation}, Volume = {19}, Year = {2014}} @article{Sharaya:2015:BIM, Author = {Irene A. Sharaya}, Journal = {Reliable Computing}, Month = {May}, Number = {4}, Pages = {435--467}, Title = {Boundary Intervals Method for Visualization of Polyhedral Solution Sets}, Volume = {19}, Year = {2015}} @article{Kolev:2014:CDI, Author = {Lyubomir V. Kolev}, Journal = {Reliable Computing}, Month = {Mar}, Number = {1}, Pages = {1--24}, Title = {Componentwise Determination of the Interval Hull Solution for Linear Interval Parameter Systems}, Volume = {20}, Year = {2014}} @article{Tapaswini:2014:NMA, Author = {Smita Tapaswini and S. Chakraverty}, Journal = {Reliable Computing}, Month = {Apr}, Number = {1}, Pages = {25--44}, Title = {New Midpoint--based Approach for the Solution of $n$--th Order Differential Equations}, Volume = {20}, Year = {2014}} @article{Rump:2014:VBP, Author = {Siegfried M. Rump}, Journal = {Reliable Computing}, Month = {Jun}, Number = {1}, Pages = {45--52}, Title = {Verified Bounds for the $p$--Norm Condition Number}, Volume = {20}, Year = {2014}} @article{Goldsztejn:2014:EIM, Author = {Alexandre Goldsztejn and Arnold Neumaier}, Journal = {Reliable Computing}, Month = {Oct}, Number = {1}, Pages = {53--72}, Title = {On the Exponentiation of Interval Matrices}, Volume = {20}, Year = {2014}} @article{Bunger:2014:NBS, Author = {Florian B{\"u}nger}, Journal = {Reliable Computing}, Month = {Oct}, Number = {1}, Pages = {73--88}, Title = {A Note on the Boundary Shape of Matrix Polytope Products}, Volume = {20}, Year = {2014}} @article{Miyajima:2015:FES, Author = {Shinya Miyajima}, Journal = {Reliable Computing}, Month = {Feb}, Number = {1}, Pages = {89--112}, Title = {Fast Enclosure for Solutions of Generalized Least Squares Problems}, Volume = {20}, Year = {2015}} @article{Shary:2015:OIS, Author = {Sergey P. Shary}, Journal = {Reliable Computing}, Month = {Mar}, Number = {1}, Pages = {113--114}, Title = {Obituary: {Irene Sharaya} (1962--2015)}, Volume = {20}, Year = {2015}} @article{Lorkowski:2015:WCW, Author = {Joe Lorkowski and Olga Kosheleva and Luc Longpr{\'e} and Vladik Kreinovich}, Journal = {Reliable Computing}, Month = {Aug}, Number = {1}, Pages = {1--10}, Title = {When Can We Reduce Multi--Variable Range Estimation Problems to Two Fewer--Variable Problems?}, Volume = {21}, Year = {2015}} @article{Ansary:2015:HOR, Author = {Md. Abu Talhamainuddin Ansary and Geetanjali Panda}, Journal = {Reliable Computing}, Month = {Sep}, Number = {1}, Pages = {11--24}, Title = {Higher Order Root Finding Algorithm using Interval Analysis}, Volume = {21}, Year = {2015}} @article{Rohn:2015:SSI, Author = {Jiri Rohn}, Journal = {Reliable Computing}, Month = {Nov}, Number = {1}, Pages = {25--34}, Title = {The Solution Set of Interval Linear Equations is Homeomorphic to the Unit Cube: {A}n Explicit Construction}, Volume = {21}, Year = {2015}} @article{Eberhart:2015:HPN, Author = {Pac{\^o}me Eberhart and Julien Brajard and Pierre Fortin and Fabienne J{\'e}z{\'e}quel}, Journal = {Reliable Computing}, Month = {Dec}, Number = {1}, Pages = {35--52}, Title = {High Performance Numerical Validation using Stochastic Arithmetic}, Volume = {21}, Year = {2015}} @article{Gioia:2016:CAP, Author = {Federica Gioia}, Journal = {Reliable Computing}, Month = {May}, Number = {1}, Pages = {53--73}, Title = {Capital Asset Pricing Model Using Regression Methods for Interval--Valued Variables}, Volume = {21}, Year = {2016}} @article{Bunger:2016:SNC, Author = {Florian B{\"u}nger and Siegfried M. Rump}, Journal = {Reliable Computing}, Month = {Jun}, Number = {1}, Pages = {74--79}, Title = {A Short Note on the Convexity of Interval Matrix--Vector Products}, Volume = {21}, Year = {2016}} @article{Markov:2016:AOI, Author = {Svetoslav Markov}, Journal = {Reliable Computing}, Month = {Jun}, Number = {1}, Pages = {80--108}, Title = {On the Algebra of Intervals}, Volume = {21}, Year = {2016}} @article{Heindl:2016:GTR, Author = {Gerd Heindl}, Journal = {Reliable Computing}, Month = {Sep}, Number = {1}, Pages = {109--116}, Title = {Generalizations of Theorems of {R}ohn and {V}rahatis}, Volume = {21}, Year = {2016}} @article{Graillat:2016:DCN, Author = {Stef Graillat and Fabienne J{\'e}z{\'e}quel and Moustadrani Sa{\"\i}d Ibrahim}, Journal = {Reliable Computing}, Month = {Oct}, Number = {1}, Pages = {117--139}, Title = {Dynamical Control of {N}ewton's Method for Multiple Roots of Polynomials}, Volume = {21}, Year = {2016}} @article{Rohn:2016:TCE, Author = {Jiri Rohn}, Journal = {Reliable Computing}, Month = {Oct}, Number = {1}, Pages = {140--145}, Title = {Theoretical Characterization of Enclosures}, Volume = {21}, Year = {2016}} @article{Garloff:2016:SCM, Author = {J{\"u}rgen Garloff and Mohammad Adm and Jihad Titi}, Journal = {Reliable Computing}, Month = {Jan}, Number = {1}, Pages = {1--14}, Title = {A Survey of Classes of Matrices Possessing the Interval Property and Related Properties}, Volume = {22}, Year = {2016}} @article{Kumkov:2016:EPC, Author = {Sergey I. Kumkov}, Journal = {Reliable Computing}, Month = {Mar}, Number = {1}, Pages = {15--25}, Title = {An Estimation Problem of Chemical Process with Confluent Parameters: {A}n Interval Approach}, Volume = {22}, Year = {2016}} @article{Kolev:2016:CIM, Author = {Lubomir V. Kolev}, Journal = {Reliable Computing}, Month = {May}, Number = {1}, Pages = {26--46}, Title = {A Class of Iterative Methods for Determining $p$--Solutions of Linear Interval Parametric Systems}, Volume = {22}, Year = {2016}} @article{Jaulin:2016:IOS, Author = {Luc Jaulin}, Journal = {Reliable Computing}, Month = {Jun}, Number = {1}, Pages = {47--55}, Title = {Inner and Outer Set--Membership State Estimation}, Volume = {22}, Year = {2016}} @article{Sandretto:2016:VSD, Author = {Julien Alexandre {dit Sandretto} and Alexandre Chapoutot}, Journal = {Reliable Computing}, Month = {Jul}, Number = {1}, Pages = {56--77}, Title = {Validated Simulation of Differential Algebraic Equations with {R}unge--{K}utta Methods}, Volume = {22}, Year = {2016}} @article{Sandretto:2016:VEI, Author = {Julien Alexandre {dit Sandretto} and Alexandre Chapoutot}, Journal = {Reliable Computing}, Month = {Jul}, Number = {1}, Pages = {79--103}, Title = {Validated Explicit and Implicit {R}unge--{K}utta Methods}, Volume = {22}, Year = {2016}} @article{Garajova:2016:SVN, Author = {Elif Garajov{\'{a}} and Martin Me{\v{c}}iar}, Journal = {Reliable Computing}, Month = {Jul}, Number = {1}, Pages = {104--115}, Title = {Solving and Visualizing Nonlinear Set Inversion Problems}, Volume = {22}, Year = {2016}} @article{Laranjeira:2016:BUM, Author = {M. Laranjeira and Luc Jaulin and S. Tauvry}, Journal = {Reliable Computing}, Month = {Aug}, Number = {1}, Pages = {116--137}, Title = {Building Underwater Mosaics Using Navigation Data and Feature Extraction}, Volume = {22}, Year = {2016}} @article{Monnet:2016:CIO, Author = {D. Monnet and J. Ninin and Luc Jaulin}, Journal = {Reliable Computing}, Month = {Sep}, Number = {1}, Pages = {138--148}, Title = {Computing an Inner and an Outer Approximation of the Viability Kernel}, Volume = {22}, Year = {2016}} @article{Hansen:2015:RMO, Author = {Eldon Hansen and Bill Walster and Sergey P. Shary and George Corliss and Luc Jaulin and Ulrich Kulisch and Michael Cloud and Louis Rall}, Journal = {Reliable Computing}, Month = {Apr}, Number = {1}, Pages = {2--14}, Title = {{Ramon Moore}: {S}hort Biography and Recollections from Close Associates}, Volume = {23}, Year = {2015}} @article{Nedialkov:2016:BMV, Author = {Nedialko S. Nedialkov and Kenneth R. Jackson and Markus Neher}, Journal = {Reliable Computing}, Month = {Jul}, Number = {1}, Pages = {15--34}, Title = {On the Blunting Method in Verified Integration of {ODE}s}, Volume = {23}, Year = {2016}} @article{Jaulin:2016:BAD, Author = {Luc Jaulin and B. Desrochers and D. Mass{\'{e}}}, Journal = {Reliable Computing}, Month = {Jul}, Number = {1}, Pages = {35--46}, Title = {Bisectable Abstract Domains for the Resolution of Equations Involving Complex Numbers}, Volume = {23}, Year = {2016}} @article{Xiao:2016:IPI, Author = {Naijia Xiao and Francesco Fedele and Rafi L. Muhanna}, Journal = {Reliable Computing}, Month = {Jul}, Number = {1}, Pages = {47--72}, Title = {Interval--Based Parameter Identification for Structural Static Problems}, Volume = {23}, Year = {2016}} @article{Yamamura:2016:FAS, Author = {Kiyotaka Yamamura and Suguru Ishiguro}, Journal = {Reliable Computing}, Month = {Jul}, Number = {1}, Pages = {73--96}, Title = {Finding All Solution Sets of Piecewise--Linear Interval Equations Using Integer Programming}, Volume = {23}, Year = {2016}} @article{Kreinovich:2016:SSG, Author = {Vladik Kreinovich}, Journal = {Reliable Computing}, Month = {Jul}, Number = {1}, Pages = {97--104}, Title = {Standing on the Shoulders of the Giants: {W}hy Constructive Mathematics, Probability Theory, Interval Mathematics, and Fuzzy Mathematics Are Important}, Volume = {23}, Year = {2016}} @article{Kreinovich:2016:IMD, Author = {Vladik Kreinovich and Sergey P. Shary}, Journal = {Reliable Computing}, Month = {Jul}, Number = {1}, Pages = {105--140}, Title = {Interval Methods for Data Fitting under Uncertainty: {A} Probabilistic Treatment}, Volume = {23}, Year = {2016}} @article{Kulisch:2016:HSA, Author = {Ulrich Kulisch and Gerd Bohlender}, Journal = {Reliable Computing}, Month = {Jul}, Number = {1}, Pages = {141--153}, Title = {High Speed Associative Accumulation of Floating--point Numbers and Floating--point Intervals}, Volume = {23}, Year = {2016}} @article{Rall:2016:IDA, Author = {Louis B. Rall}, Journal = {Reliable Computing}, Month = {Jul}, Number = {1}, Pages = {154--162}, Title = {Interval Divided--Difference Arithmetic}, Volume = {23}, Year = {2016}} @article{Goldsztejn:2016:PMH, Author = {Alexandre Goldsztejn and Daisuke Ishii}, Journal = {Reliable Computing}, Month = {Jul}, Number = {1}, Pages = {163--185}, Title = {A Parallelotope Method for Hybrid System Simulation}, Volume = {23}, Year = {2016}} @Article {Mullier:2017:SMC, author = {Olivier Mullier and Estelle Courtial}, title = {Set-Membership Computation of Admissible Controls for Trajectory Tracking}, journal = {Reliable Computing}, number = {1}, month = {Apr}, year = {2017}, pages = {11--26}, volume = {24} } @Article {Kreinovich:2017:RCF, author = {Vladik Kreinovich and Olga Kosheleva}, title = {The Range of a Continuous Functional Under Set-Valued Uncertainty is Always an Interval}, journal = {Reliable Computing}, number = {1}, month = {May}, year = {2017}, pages = {27--30}, volume = {24} } @Article {Miyajima:2017:VSI, author = {Shinya Miyajima}, title = {Verified Solutions of Inverse Symmetric Eigenvalue Problems}, journal = {Reliable Computing}, number = {1}, month = {Sep}, year = {2017}, pages = {31--44}, volume = {24} } @Article {Olague:2017:WSPBE, author = {Pedro A. Barragan Olague and Vladik Kreinovich}, title = {Why Superellipsoids: {A} Probability-Based Explanation}, journal = {Reliable Computing}, number = {1}, month = {May}, year = {2017}, pages = {1--7}, volume = {25} } @Article {Afravi:2017:DMU, author = {Mahdokht Michelle Afravi and Vladik Kreinovich}, title = {Decision Making Under Interval Uncertainty as a Natural Example of a Quandle}, journal = {Reliable Computing}, number = {1}, month = {May}, year = {2017}, pages = {8--14}, volume = {25} } @Article {Titi:2017:FDT, author = {Jihad Titi and J{\"u}rgen Garloff}, title = {Fast Determination of the Tensorial and Simplicial {B}ernstein Forms of Multivariate Polynomials and Rational Functions}, journal = {Reliable Computing}, number = {1}, month = {Jun}, year = {2017}, pages = {24--37}, volume = {25} } @Article {Graillat:2017:MDM, author = {Stef Graillat and Clothilde Jeangoudoux and Christoph Lauter}, title = {{MPDI}: {A} Decimal Multiple-Precision Interval Arithmetic Library}, journal = {Reliable Computing}, number = {1}, month = {Jul}, year = {2017}, pages = {38--52}, volume = {25} } @Article {Karhbet:2017:RBF, author = {Sam Karhbet and Ralph Baker Kearfott}, title = {Range Bounds of Functions over Simplices, for Branch and Bound Algorithms}, journal = {Reliable Computing}, number = {1}, month = {Jul}, year = {2017}, pages = {53--73}, volume = {25} } @Article {Takayasu:2017:AMV, author = {Akitoshi Takayasu and Makoto Mizuguchi and Takayuki Kubo and Shin'ichi Oishia}, title = {Accurate Method of Verified Computing for Solutions of Semilinear Heat Equation}, journal = {Reliable Computing}, number = {1}, month = {Jul}, year = {2017}, pages = {74--99}, volume = {25} } @Article {Rauh:2017:IBA, author = {Andreas Rauh and Susann Tiede and Cornelia Klenke}, title = {An Interval-Based Algorithm for Feature Extraction from Speech Signals}, journal = {Reliable Computing}, number = {1}, month = {Aug}, year = {2017}, pages = {100--117}, volume = {25} } @Article {Rauh:2017:TOP, author = {Andreas Rauh and Julia Kersten and Harald Aschemann}, title = {Toward the Optimal Parameterization of Interval-Based Variable-Structure State Estimation Procedures}, journal = {Reliable Computing}, number = {1}, month = {Aug}, year = {2017}, pages = {118--132}, volume = {25} } @Article {Rauh:2017:IBI, author = {Andreas Rauh and Julia Kersten and Harald Aschemann}, title = {Interval-Based Identification of Friction and Hysteresis Models}, journal = {Reliable Computing}, number = {1}, month = {Aug}, year = {2017}, pages = {133--147}, volume = {25} } @Article {Ozaki:2017:GLS, author = {Katsuhisa Ozaki and Takeshi Ogita}, title = {Generation of Linear Systems with Specified Solutions for Numerical Experiments}, journal = {Reliable Computing}, number = {1}, month = {Aug}, year = {2017}, pages = {148--167}, volume = {25} } @Article {Kinoshita:2017:VCE, author = {Takehiko Kinoshita and Yoshitaka Watanabe and Mitsuhiro T. Nakao}, title = {Validated Constructive Error Estimations for Biharmonic Problems}, journal = {Reliable Computing}, number = {1}, month = {Aug}, year = {2017}, pages = {168--177}, volume = {25} } @Article {Sandretto:2017:RKTCP, author = {Julien Alexandre dit Sandretto}, title = {{R}unge-{K}utta Theory and Constraint Programming}, journal = {Reliable Computing}, number = {1}, month = {Augj}, year = {2017}, pages = {178--201}, volume = {25} } @Article {Kimura:2017:OOC, author = {Takuma Kimura and Teruya Minamoto and Mitsuhiro T. Nakao}, title = {Optimal Order Constructive a Priori Error Estimates for a Full Discrete Approximation of the Heat Equation}, journal = {Reliable Computing}, number = {1}, month = {Sep}, year = {2017}, pages = {202--212}, volume = {25} } @Article {Keyanpour:2018:SAS, author = {Mohammad Keyanpour and Maryam Mohaghegh Tabar and Weldon A. Lodwick}, title = {A Solution Algorithm for a System of Interval Linear Equations Based on the Constraint Interval Point of View}, journal = {Reliable Computing}, number = {1}, month = {Feb}, year = {2018}, pages = {1--12}, volume = {26} } @Article {Imbach:2018:RLR, author = {R{\'e}mi Imbach and Guillaume Moroz and Marc Pouget}, title = {Reliable Location with Respect to the Projection of a Smooth Space Curve}, journal = {Reliable Computing}, number = {1}, month = {May}, year = {2018}, pages = {13--55}, volume = {26} } @Article {Rump:2018:LSMZR, author = {Siegfried M. Rump}, title = {Linear Systems in {M}atlab with Zero Residual}, journal = {Reliable Computing}, number = {1}, month = {Jun}, year = {2018}, pages = {56--66}, volume = {26} } @Article {M.-Alizadeh:2018:IGSA, author = {Benyamin M.-Alizadeh and Sajjad Rahmany and Abdolali Basiri}, title = {Interval {G}r{\"{o}}bner System and its Applications}, journal = {Reliable Computing}, number = {1}, month = {Jun}, year = {2018}, pages = {67--96}, volume = {26} } @Article {Rohn:2017:EEC, author = {Jiri Rohn}, title = {An Explicit Enclosure of the Solution Set of Overdetermined Interval Linear Equations}, journal = {Reliable Computing}, number = {1}, month = {Feb}, year = {2017}, pages = {1--10}, volume = {24} }