Error estimates for interpolation by compactly supported radial basis functions of minimal degree

Wendland, Holger (1998) Error estimates for interpolation by compactly supported radial basis functions of minimal degree. Journal of Approximation Theory, 93 (2). pp. 258-272. ISSN 0021-9045

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Abstract

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.

Item Type: Article
Schools and Departments: School of Mathematical and Physical Sciences > Mathematics
Depositing User: Holger Wendland
Date Deposited: 06 Feb 2012 19:11
Last Modified: 09 Jul 2012 13:19
URI: http://sro.sussex.ac.uk/id/eprint/19521
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