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Error estimates for scattered data interpolation on spheres

Authors: Kurt Jetter, Joachim Stöckler and Joseph D. Ward
Journal: Math. Comp. 68 (1999), 733-747
MSC (1991): Primary 41A05, 41A25; Secondary 41A30, 41A63
MathSciNet review: 1642746
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Abstract: We study Sobolev type estimates for the approximation order resulting from using strictly positive definite kernels to do interpolation on the $n$-sphere. The interpolation knots are scattered. Our approach partly follows the general theory of Golomb and Weinberger and related estimates. These error estimates are then based on series expansions of smooth functions in terms of spherical harmonics. The Markov inequality for spherical harmonics is essential to our analysis and is used in order to find lower bounds for certain sampling operators on spaces of spherical harmonics.

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Additional Information

Kurt Jetter
Affiliation: Institut für Angewandte Mathematik und Statistik, Universität Hohenheim, D-70593 Stuttgart

Joachim Stöckler
Affiliation: Institut für Angewandte Mathematik und Statistik, Universität Hohenheim, D-70593 Stuttgart

Joseph D. Ward
Affiliation: Department of Mathematics, Texas A&M University, College Station, TX 77843

Keywords: Scattered data interpolation, spherical harmonics, Markov inequality, norming set, best approximation
Received by editor(s): August 25, 1997
Additional Notes: Research supported by NSF Grant DMS-9303705 and Air Force AFOSR Grant F49620-95-1-0194.
Article copyright: © Copyright 1999 American Mathematical Society

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