Sparse interpolation and rational approximationSparse interpolation and rational approximation
Faculty of Sciences. Mathematics and Computer Science

Computational Mathematics

conferenceObject

2016Providence :Amer mathematical soc, 2016

Mathematics

Contemporary mathematics / American Mathematical Society. - Providence, R.I.

Conference and School on Constructive Functions in honor of Ed Saff's, 70th Birthday, MAY 26-30, 2014, Vanderbilt Univ, Vanderbilt Univ, Nashville, TN

661(2016), p. 229-242

0271-4132

978-1-4704-2534-0

000378008700014

E

English (eng)

University of Antwerp

Sparse interpolation or exponential analysis, is widely used and in quite different applications and areas of science and engineering. Therefore researchers are often not aware of similar studies going on in another field. The current text is written as a concise tutorial, from an approximation theorist point of view. In Section 2 we summarize the mathematics involved in exponential analysis: structured matrices, generalized eigenvalue problems, singular value decomposition. The section is written with the numerical computation of the sparse interpolant in mind. In Section 3 we outline several connections of sparse interpolation with other mostly non-numeric subjects: computer algebra, number theory, linear recurrences. Some problems are only solved using exact arithmetic. In Section 4 we connect sparse interpolation to rational approximation theory. One of the major hurdles in sparse interpolation is still the correct detection of the number of components in the model. Here we show how to reliably obtain the number of terms in a numeric and noisy environment. The new insight allows to improve on existing state-of-the-art algorithms.

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