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\begin{document}

\title{Recent Results on Symmetric Interval Systems}
\author{G\"otz Alefeld$^1$ and G\"unter Mayer$^2$}

\pagestyle{myheadings}

\markright{APIC'95, El Paso,
Extended Abstracts,
A Supplement to the international journal of {\rm Reliable
Computing}\ \ \ \ \ \ \ \ \ \ \  \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \
\ \ \ \ \ \ \ \ \ \ \ \ \ }

\maketitle

\begin{abstract}
We consider the solution set $S$ of real linear systems $Ax=b$ with
the $n\times n$ coefficient matrix $A$ varying between a lower bound
$\underline A$ and an upper bound $\overline A$, and with $b$
similarly varying between $\underline b$ and $\overline b$. 
\begin{itemize}
\smallskip

\item First, we
list some properties on the shape of $S$ if all matrices $A$ are
non-singular. 
\smallskip

\item Then, we restrict $A$ to be nonsingular and symmetric,
and for $n=2$, derive a complete description of the boundary of the
corresponding symmetric solution set $S_{sym}$. 
\smallskip

\item Finally, we derive a new criterion for the feasibility of the Cholesky
method with which one can find bounds for $S_{sym}$. 
\end{itemize}
\end{abstract} 
  
\auffil{The authors are with 
$^1$Inst. fur Angewandte Mathematik,
University of Karlsruhe,
76128 Karlsruhe,
Germany,
email goetz.alefeld@math.uni-karlsruhe.de, and with 
$^2$Fachbereich Mathematik,
Universit"at Rostock,
D-18051 Rostock,
Germany,
email guenter.mayer@mathematik.uni-rostock.de.}

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