Lp-error estimates for radial basis function interpolation on the sphere

Authors:
Simon Hubbert;Tanya M. Morton
Affiliations:
Lehrstuhl für Numerische Mathematik, Justus-Liebig-Universität, Heinrich-Buff-Ring 44, Giessen 35392, Germany;The Mathworks Ltd, Matrix House, Cowley Park, Cambridge CB4 0HH, UK
Venue:
Journal of Approximation Theory
Year:
2004

Citing 5
Cited 6

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Abstract

In this paper we review the variational approach to radial basis function interpolation on the sphere and establish new Lp-error bounds, for p ∈ [1, ∞]. These bounds are given in terms of a measure of the density of the interpolation points, the dimension of the sphere and the smoothness of the underlying basis function.