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Error estimates in the fast multipole method for scattering problems. I. Truncation of the Jacobi-Anger series. (English) Zbl 1077.41027
This paper is the first one of a series of three addressing the analysis of the error in the fast multipole method (FMM) for scatering problems. It is maked a complete study of the truncation error of the Jacobi-Anger series. Numerical experiments show that this asymptotic is optimal. Those results are useful to provide sharp estimates for the error in the fast multiple method for scattering computation. Since from the pionier work of Rokhlin, the FMM has been proved to be a very effective tool for solving three-dimensional acoustic or electromagnetic scattering problems.

MSC:
41A80 Remainders in approximation formulas
33C10 Bessel and Airy functions, cylinder functions, \({}_0F_1\)
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