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Direct and Inverse Sobolev Error Estimates for Scattered Data Interpolation via Spherical Basis Functions

Foundations of Computational Mathematics volume 7, pages 369–390 (2007)Cite this article

Abstract

The purpose of this paper is to get error estimates for spherical basis function (SBF) interpolation and approximation for target functions in Sobolev spaces less smooth than the SBFs, and to show that the rates achieved are, in a sense, best possible. In addition, we establish a Bernstein-type theorem, where the smallest separation between data sites plays the role of a Nyquist frequency. We then use these Berstein-type estimates to derive inverse estimates for interpolation via SBFs.

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Authors and Affiliations

  1. Department of Mathematics, Texas A&M University, College Station, TX 77843, USA

    Francis J. Narcowich & Joseph D. Ward

  2. Department of Mathematics, Southwest Missouri State University, Springfield, MO 65804, USA

    Xingping Sun

  3. Universitat Gottingen, Lotzestrasse 16-18, D-37083, Gottingen, Germany

    Holger Wendland

Authors
  1. Francis J. Narcowich
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  2. Xingping Sun
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  3. Joseph D. Ward
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  4. Holger Wendland
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Narcowich, F., Sun, X., Ward, J. et al. Direct and Inverse Sobolev Error Estimates for Scattered Data Interpolation via Spherical Basis Functions. Found Comput Math 7, 369–390 (2007). https://doi.org/10.1007/s10208-005-0197-7

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  • DOI: https://doi.org/10.1007/s10208-005-0197-7

Keywords

  • Radial Basis Function
  • Sobolev Space
  • Target Function
  • Reproduce Kernel Hilbert Space
  • Native Space