Preprint 15/2005

Approximation of 1∥x- y∥ by Exponentials for Wavelet Applications

Wolfgang Hackbusch

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Submission date: 22. Feb. 2005 (revised version: June 2005)
Pages: 7
published in: Computing, 76 (2006) 3-4, p. 359-366 
DOI number (of the published article): 10.1007/s00607-005-0134-2
MSC-Numbers: 41A50, 65T60, 11L07
Keywords and phrases: approximation by exponentials, wavelets
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We discuss the approximation of formula6 by exponentials in order to apply it to the treatment of formula8. In the case of a wavelet basis, one has in addition the vanishing moment property, which allows to add polynomials without increasing the computational effort. This leads to the question whether an approximation of formula6 by the sum of a polynomial and an exponential part yields an improvement. We show that indeed the approximation error is remarkably reduced. The improvement depends on the interval on which formula6 is approximated.

18.10.2019, 02:12