Extending the Range of Error Estimates for Radial Approximation in Euclidean Space and on Spheres

We adapt Schaback's error doubling trick [R. Schaback, Math. Comp., 68 (1999), pp. 201-216] to give error estimates for radial interpolation of functions with smoothness lying (in some sense) between that of the usual native space and the subspace with double the smoothness. We do this for both...

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Bibliographic Details
Published inSIAM journal on mathematical analysis Vol. 39; no. 2; pp. 554 - 564
Main Authors Brownlee, R. A., Georgoulis, E. H., Levesley, J.
Format Journal Article
LanguageEnglish
Published Philadelphia Society for Industrial and Applied Mathematics 01.01.2007
Subjects
Approximation
Estimates
Euclidean space
Hilbert space
Spheres
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Summary:We adapt Schaback's error doubling trick [R. Schaback, Math. Comp., 68 (1999), pp. 201-216] to give error estimates for radial interpolation of functions with smoothness lying (in some sense) between that of the usual native space and the subspace with double the smoothness. We do this for both bounded subsets of ${\mathbb{R}}^d$ and spheres. As a step on the way to our ultimate goal we also show convergence of pseudoderivatives of the interpolation error.
ISSN:0036-1410
1095-7154
DOI:10.1137/060650428