Title 



Sparse interpolation and rational approximation
 
Author 



 
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 nonnumeric 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 stateoftheart algorithms.   
Language 



English
 
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 2630, 2014, Vanderbilt Univ, Vanderbilt Univ, Nashville, TN  
Publication 



Providence : Amer mathematical soc, 2016
 
Volume/pages 



661(2016), p. 229242
 
ISI 



000378008700014
 
Number 



9781470425340
 
Full text (Publishers DOI) 


  
