The Eigenvalues of Matrices That Occur in Certain Interpolation Problems (1997)
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@MISC{Ferreira97theeigenvalues,
author = {Paulo J. S. G. Ferreira},
title = {The Eigenvalues of Matrices That Occur in Certain Interpolation Problems},
year = {1997}
}
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Abstract
The eigenvalues of the matrices that occur in certain finite-dimensional interpolation problems are directly related to their well-posedness, and strongly depend on the distribution of the interpolation knots, that is, on the sampling set. We study this dependency as a function of the sampling set itself, and give accurate bounds for the eigenvalues of the interpolation matrices. The bounds can be evaluated in as few as four arithmetic operations, and so they greatly simplify the assessment of sampling sets regarding numerical stability. The accuracy and usefulness of the bounds are illustrated with examples. I. Introduction One problem commonly found in signal processing is that of recovering n lost samples of a band-limited discrete signal with a total of N samples. The Papoulis-Gerchberg algorithm [1, 2], although initially developed for extrapolation problems, is a well-known example of an iterative technique that can be used to solve this problem. It is related to a number ...
