Error Estimates for Interpolation by Compactly Supported Radial Basis Functions of Minimal Degree
نویسنده
چکیده
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. AMS classi cations: 41A05, 41A15, 41A30, 41A63, 65D05.
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