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“Approximate approximations” and the cubature of potentials. (English) Zbl 0845.65008
A new method is given for the approximation of singular integrals that arise in potential theory. The basic idea is to approximate the integrand using quasi interpolants constructed using integrand values at points on a regular mesh. The basis functions for the interpolation are products of generalized Laguerre polynomials and a Gaussian weight. For harmonic, elastic and diffraction potentials, this choice of basis function allows the authors to derive explicit formulas for the approximations to the singular integrals. Error analysis is given which provides error bounds for these basis functions, and more general basis functions. Some numerical results are given for the harmonic potential.
Reviewer: A.C.Genz (Pullman)

65D32 Numerical quadrature and cubature formulas
41A55 Approximate quadratures
41A63 Multidimensional problems
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