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Error Estimates for Interpolation by Compactly Supported Radial Basis Functions of Minimal Degree

1998; Elsevier BV; Volume: 93; Issue: 2 Linguagem: Inglês

10.1006/jath.1997.3137

1096-0430

Holger Wendland,

Advanced Numerical Methods in Computational Mathematics

We consider error estimates for interpolation by a special class of compactly supported radial basis functions. These functions consist of a univariate polynomial within their support and are of minimal degree depending on space dimension and smoothness. Their associated “native” Hilbert spaces are shown to be norm-equivalent to Sobolev spaces. Thus we can derive approximation orders for functions from Sobolev spaces which are comparable to those of thin-plate-spline interpolation. Finally, we investigate the numerical stability of the interpolation process.