Interpolation on the sphere: a fast solution technique

Abstract

We present a fast solution technique for the problem of interpolation on the sphere, using radial basis functions and multiplicative Schwarz methods. This problem has applications in geodesy and earth science. A bound for the condition number of the preconditioned matrix is proved. Since approximation using radial basis functions is a meshless method, the proof technique is novel compared to that used in finite element methods. Numerical experiments on relatively large sets of scattered data points taken from magsat satellite data are presented. The article illustrates how interpolation of scattered data on the sphere can be efficiently performed.