Wendland functions with increasing smoothness converge to a Gaussian

Authors:
A. Chernih;I. H. Sloan;R. S. Womersley
Affiliations:
School of Mathematics and Statistics, University of New South Wales, Sydney, Australia 2052;School of Mathematics and Statistics, University of New South Wales, Sydney, Australia 2052;School of Mathematics and Statistics, University of New South Wales, Sydney, Australia 2052
Venue:
Advances in Computational Mathematics
Year:
2014

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Abstract

The Wendland functions are a class of compactly supported radial basis functions with a user-specified smoothness parameter. We prove that with an appropriate rescaling of the variables, both the original and the "missing" Wendland functions converge uniformly to a Gaussian as the smoothness parameter approaches infinity. We also explore the convergence numerically with Wendland functions of different smoothness.