Polynomials and potential theory for Gaussian radial basis function interpolation

Rodrigo B. Platte, Tobin A. Driscoll

Research output: Contribution to journalArticle

43 Scopus citations

Abstract

We explore a connection between Gaussian radial basis functions and polynomials. Using standard tools of potential theory, we find that these radial functions are susceptible to the Runge phenomenon, not only in the limit of increasingly flat functions, but also in the finite shape parameter case. We show that there exist interpolation node distributions that prevent such phenomena and allow stable approximations. Using polynomials also provides an explicit interpolation formula that avoids the difficulties of inverting interpolation matrices, while not imposing restrictions on the shape parameter or number of points.

Original languageEnglish (US)
Pages (from-to)750-766
Number of pages17
JournalSIAM Journal on Numerical Analysis
Volume43
Issue number2
DOIs
StatePublished - Dec 1 2005

Keywords

  • Convergence
  • Gaussian radial basis functions
  • Potential theory
  • RBF
  • Runge phenomenon
  • Stability

ASJC Scopus subject areas

  • Numerical Analysis
  • Computational Mathematics
  • Applied Mathematics

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