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MiS Preprint
15/2005
Approximation of $1/\left\Vert x-y\right\Vert $ by Exponentials for Wavelet Applications
Wolfgang Hackbusch
Abstract
We discuss the approximation of $1/\sqrt{t}$ by exponentials in order to apply it to the treatment of $1/\left\Vert x-y\right\Vert $. 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 $1/\sqrt{t}$ 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 $1/\sqrt{t}$ is approximated.
