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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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Inf-sup condition for spherical polynomials and radial basis functions on spheres
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by Ian H. Sloan and Holger Wendland PDF
Math. Comp. 78 (2009), 1319-1331 Request permission


Interpolation by radial basis functions and interpolation by polynomials are both popular methods for function reconstruction from discrete data given on spheres. Recently, there has been an increasing interest in employing these function families together in hybrid schemes for scattered data modeling and the solution of partial differential equations on spheres. For the theoretical analysis of numerical methods for the associated discretized systems, a so-called inf-sup condition is crucial. In this paper, we derive such an inf-sup condition, and show that the constant in the inf-sup condition is independent of the polynomial degree and of the chosen point set, provided the mesh norm of the point set is sufficiently small. We then use the inf-sup condition to derive a new error analysis for the hybrid interpolation scheme of Sloan and Sommariva.
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Additional Information
  • Ian H. Sloan
  • Affiliation: School of Mathematics and Statistics, University of New South Wales, Sydney, NSW, 2052, Australia
  • MR Author ID: 163675
  • ORCID: 0000-0003-3769-0538
  • Email:
  • Holger Wendland
  • Affiliation: Department of Mathematics, University of Sussex, Brighton, BN1 9RF, England
  • MR Author ID: 602098
  • Email:
  • Received by editor(s): December 17, 2007
  • Received by editor(s) in revised form: August 6, 2008
  • Published electronically: January 22, 2009
  • © Copyright 2009 American Mathematical Society
  • Journal: Math. Comp. 78 (2009), 1319-1331
  • MSC (2000): Primary 65D05; Secondary 41A05, 41A29
  • DOI:
  • MathSciNet review: 2501052