Adaptive Least Squares Fitting with Radial Basis Functions on the Sphere

. We investigate adaptive least squares approximation to scattered data given over the surface of the unit sphere in IR 3 . Two basic algorithms (as well as some modifications) are described and evaluated: knot insertion and knot removal. x1. Introduction Since their introduction by R. L. Hardy in the 1970s, radial basis functions have become a standard tool in CAGD and approximation theory for the construction of surfaces interpolating and approximating scattered data. Most of the work on scattered data approximation with radial basis functions has been in the Euclidean setting (see e.g. [4], and some references therein). On the sphere interpolation was treated e.g. in [1,3,7,8]. So far there has been no discussion of the use of radial basis functions for approximation over the sphere. This, however, is a problem of great interest in many areas of the applied sciences, in particular geodesy and meteorology. The purpose of this paper is to investigate adaptive approximation to scatt..