Fitting scattered data on sphere-like surfaces using spherical splines
Journal of Computational and Applied Mathematics - Special issue on scattered data
Scattered data fitting on the sphere
Proceedings of the international conference on Mathematical methods for curves and surfaces II Lillehammer, 1997
Fast Solution of the Radial Basis Function Interpolation Equations: Domain Decomposition Methods
SIAM Journal on Scientific Computing
Overlapping domain decomposition method by radial basis functions
Applied Numerical Mathematics
Foundations of Computational Mathematics
Preconditioning for radial basis functions with domain decomposition methods
Mathematical and Computer Modelling: An International Journal
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The problem of interpolation of scattered data on the unit sphere has many applications in geodesy and Earth science in which the sphere is taken as a model for the Earth. Spherical radial basis functions provide a convenient tool for constructing the interpolant. However, the underlying linear systems tend to be ill-conditioned. In this paper, we present an additive Schwarz preconditioner for accelerating the solution process. An estimate for the condition number of the preconditioned system will be discussed. Numerical experiments using MAGSAT satellite data will be presented.