A Fast Algorithm for Spherical Basis Approximation

What is it about?

Radial basis functions appear in a wide field of applications in numerical mathematics and computer science. We present a fast algorithm for scattered data interpolation and approximation on the sphere with spherical radial basis functions of different spatial density. We discuss three settings, each leading to a special structure of the interpolation matrix allowing for an efficient implementation using discrete Fourier transforms. A numerical example is given to show the advantages of spherical radial basis functions with different spatial densities.

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