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.), <I>Bounding Approaches to System
Identification</I>. Plenum Press, N.Y., 1996, 139-157.
<P>

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. 
<P>

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.
<P>

S. M. Markov and E. D. Popova