Error estimates for two-dimensional Cross Approximation

Jan Schneider

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Submission date: 09. Jan. 2009
Pages: 20
published in: Journal of approximation theory, 162 (2010) 9, p. 1685-1700 
DOI number (of the published article): 10.1016/j.jat.2010.04.012
Bibtex
MSC-Numbers: 65G99, 68W25, 41A50
Keywords and phrases: Cross Approximation, error estimates, best approximation, bilinear forms
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Abstract:
We deal with the approximation of a given function f on by special bilinear forms via the so-called cross approximation. In particular we are interested in estimating the error function of the corresponding algorithm in the maximum norm. Because of the large amount of papers available that deal with similar matrix algorithms in applied situations without giving satisfactory error estimates, we concentrate on the theoretical issues of the problem in the language of functions. We connect it with related results from other areas of Analysis in an historical survey and give a lot of references. Our main result is the connection of the error of our algorithm with the error of best approximation by arbitrary bilinear forms.