Approximation of scattered data by trigonometric polynomials on the torus and the 2-sphere

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Fast, efficient and reliable algorithms for the discrete least-square approximation of scattered points on the torus Td and the sphere S2 by trigonometric polynomials are presented. The algorithms are based on iterative CG-type methods in combination with fast Fourier transforms for nonequispaced data. The emphasis is on numerical aspects, in order to solve large scale problems. Numerical examples show the efficiency of the new algorithms.

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