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Constructive Approximation

, Volume 17, Issue 1, pp 1–18 | Cite as

Interpolation by Polynomials and Radial Basis Functions on Spheres

  • M. v. Golitschek
  • W. A. Light
Article

Abstract.

The paper obtains error estimates for approximation by radial basis functions on the sphere. The approximations are generated by interpolation at scattered points on the sphere. The estimate is given in terms of the appropriate power of the fill distance for the interpolation points, in a similar manner to the estimates for interpolation in Euclidean space. A fundamental ingredient of our work is an estimate for the Lebesgue constant associated with certain interpolation processes by spherical harmonics. These interpolation processes take place in ``spherical caps'' whose size is controlled by the fill distance, and the important aim is to keep the relevant Lebesgue constant bounded. This result seems to us to be of independent interest.

Key words. Radial basis functions, Spheres, Interpolation, Error estimates, Spherical harmonics. AMS Classification. 41A05, 41A25, 41A63. 

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Copyright information

© Springer-Verlag New York Inc. 2000

Authors and Affiliations

  • M. v. Golitschek
    • 1
  • W. A. Light
    • 1
  1. 1.Institut für Angewandte Mathematik und Statistik Universität Würzburg Am Hubland 97074 Würzburg GermanyDE

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