Error Estimates for Interpolation By Compactly Supported Radial Basis Functions of Minimal Degree (1997)
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BibTeX
@MISC{Wendland97errorestimates,
author = {Holger Wendland},
title = {Error Estimates for Interpolation By Compactly Supported Radial Basis Functions of Minimal Degree},
year = {1997}
}
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Abstract
We consider error estimates for the 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.
