Abstract
We discuss the approximation of 
by exponentials in order to apply it to the treatmentof 1/||x-y||. 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 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 is approximated.
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References
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W. Hackbusch (2001) ArticleTitleThe efficient computation of certain determinants arising in the treatment of Schrödinger's equation Computing 67 35–56 Occurrence Handle10.1007/s006070170015 Occurrence Handle0997.65075 Occurrence Handle2002g:65050
A. K. Louis P. Maaß A. Rieder (1998) Wavelets Teubner Stuttgart
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Hackbusch, W. Approximation of 1/||x−y|| by Exponentials for Wavelet Applications (Short Communication). Computing 76, 359–366 (2006). https://doi.org/10.1007/s00607-005-0134-2
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DOI: https://doi.org/10.1007/s00607-005-0134-2