Please use this identifier to cite or link to this item: http://hdl.handle.net/1893/29111
Appears in Collections:Computing Science and Mathematics Conference Papers and Proceedings
Author(s): Cuyt, Annie
Lee, Wen-shin
Contact Email: wen-shin.lee@stir.ac.uk
Title: Sparse interpolation and rational approximation
Editor(s): Hardin, DP
Lubinsky, DS
Simanek, BZ
Citation: Cuyt A & Lee W (2016) Sparse interpolation and rational approximation. In: Hardin D, Lubinsky D & Simanek B (eds.) Modern Trends in Constructive Function Theory. Contemporary Mathematics, 661. Constructive Functions 2014 - Conference in Honor of Ed Saff's 70th Birthday, Nashville, TN, USA, 26.05.2014-30.05.2014. Providence, RI, USA, pp. 229-242. https://bookstore.ams.org/conm-661
Issue Date: 2016
Series/Report no.: Contemporary Mathematics, 661
Conference Name: Constructive Functions 2014 - Conference in Honor of Ed Saff's 70th Birthday
Conference Dates: 2014-05-26 - 2014-05-30
Conference Location: Nashville, TN, USA
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.
Status: AM - Accepted Manuscript
Rights: The publisher has not responded to our queries therefore this work cannot be made publicly available in this Repository. Please use the Request a Copy feature at the foot of the Repository record to request a copy directly from the author. You can only request a copy if you wish to use this work for your own research or private study.
URL: https://bookstore.ams.org/conm-661

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