AN ADAPTIVE HIERARCHICAL APPROXIMATION METHOD ON THE SPHERE USING AXISYMMETRICAL LOCALLY SUPPORTED BASIS FUNCTIONS

The paper discusses the approximation of scattered data on the sphere which is one of the major tasks in geomathematics. Starting from the d iscretization of singular integrals on the sphere the authors devise a simple approximation method that employs locally supported spherical polynomials and does not require equidistributed grids. It is the basi s for a hierarchical approximation algorithm using differently scaled basis functions, adaptivity and error control. The method is applied t o two examples one of which is a digital terrain model of Australia.