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Advances in Computational Mathematics

, Volume 23, Issue 3, pp 317–330 | Cite as

Near-optimal data-independent point locations for radial basis function interpolation

  • Stefano De Marchi
  • Robert Schaback
  • Holger Wendland
Article

Abstract

The goal of this paper is to construct data-independent optimal point sets for interpolation by radial basis functions. The interpolation points are chosen to be uniformly good for all functions from the associated native Hilbert space. To this end we collect various results on the power function, which we use to show that good interpolation points are always uniformly distributed in a certain sense. We also prove convergence of two different greedy algorithms for the construction of near-optimal sets which lead to stable interpolation. Finally, we provide several examples.

Keywords

radial basis function interpolation optimal points greedy algorithms 

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Copyright information

© Springer 2005

Authors and Affiliations

  • Stefano De Marchi
    • 1
  • Robert Schaback
    • 2
  • Holger Wendland
    • 2
  1. 1.University of VeronaVeronaItaly
  2. 2.Universität GöttingenGöttingenGermany

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