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://srodev.sussex.ac.uk/id/eprint/19521

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