Error bounds for anisotropic RBF interpolation

Authors:
Rick Beatson;Oleg Davydov;Jeremy Levesley
Affiliations:
Department of Mathematics and Statistics, University of Canterbury, Private Bag 4800, Christchurch, New Zealand;Department of Mathematics, University of Strathclyde, 26 Richmond Street, Glasgow G1 1XH, Scotland, United Kingdom;Department of Mathematics, University of Leicester, Leicester LE1 7RH, England, United Kingdom
Venue:
Journal of Approximation Theory
Year:
2010

Citing 2
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Computers & Mathematics with Applications

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Abstract

We present error bounds for the interpolation with anisotropically transformed radial basis functions for both a function and its partial derivatives. The bounds rely on a growth function and do not contain unknown constants. For polyharmonic basic functions in R^2, we show that the anisotropic estimates predict a significant improvement of the approximation error if both the target function and the placement of the centers are anisotropic, and this improvement is confirmed numerically.