Title
Sparse interpolation and rational approximation
Author
Faculty/Department
Faculty of Sciences. Mathematics and Computer Science
Publication type
conferenceObject
Publication
Providence :Amer mathematical soc ,
Subject
Mathematics
Source (journal)
Contemporary mathematics / American Mathematical Society. - Providence, R.I.
Source (book)
Conference and School on Constructive Functions in honor of Ed Saff's, 70th Birthday, MAY 26-30, 2014, Vanderbilt Univ, Vanderbilt Univ, Nashville, TN
Volume/pages
661(2016) , p. 229-242
ISSN
0271-4132
ISBN
978-1-4704-2534-0
ISI
000378008700014
Carrier
E
Target language
English (eng)
Full text (Publishers DOI)
Affiliation
University of Antwerp
Abstract
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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