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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.98.

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Error estimates for scattered data interpolation on spheres
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by Kurt Jetter, Joachim Stöckler and Joseph D. Ward PDF
Math. Comp. 68 (1999), 733-747 Request permission

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
  • Email: kjetter@uni-hohenheim.de
  • Joachim Stöckler
  • Affiliation: Institut für Angewandte Mathematik und Statistik, Universität Hohenheim, D-70593 Stuttgart
  • Email: stockler@uni-hohenheim.de
  • Joseph D. Ward
  • Affiliation: Department of Mathematics, Texas A&M University, College Station, TX 77843
  • MR Author ID: 180590
  • Email: jward@math.tamu.edu
  • 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.
  • © Copyright 1999 American Mathematical Society
  • Journal: Math. Comp. 68 (1999), 733-747
  • MSC (1991): Primary 41A05, 41A25; Secondary 41A30, 41A63
  • DOI: https://doi.org/10.1090/S0025-5718-99-01080-7
  • MathSciNet review: 1642746