S. M. Markov and E. D. Popova, "Linear Interpolation and Estimation using Interval Analysis", In: M. Milanese, J. P. Norton, H. P.-Lahanier, and E. Walter (eds.), Bounding Approaches to System Identification. Plenum Press, N.Y., 1996, 139-157.

We consider the problems of interpolation and curve fitting in the presence of unknown but bounded errors in the output measurements. The modeling function is a {\it generalized polynomial}, i.e., an expression of the type $\sum_{i=1}^m\lambda_i \varphi _i(\vec x)$, where $\varphi_i(\vec x)$ are given functions, and $\lambda_i$ are parameters to be determined.

We characterize and present the bounding functions for the solution set using interval arithmetic. Numerical algorithms with result verification and corresponding programs for the computation of the bounding functions in given domain are reported and some examples are presented.

S. M. Markov and E. D. Popova