A new class of oscillatory radial basis functions

B. Fornberg, E. Larsson, G. Wright

Research output: Contribution to journalArticlepeer-review

54 Scopus citations

Abstract

Radial basis functions (RBFs) form a primary tool for multivariate interpolation, and they are also receiving increased attention for solving PDEs on irregular domains. Traditionally, only nonoscillatory radial functions have been considered. We find here that a certain class of oscillatory radial functions (including Gaussians as a special case) leads to nonsingular interpolants with intriguing features especially as they are scaled to become increasingly flat. This flat limit is important in that it generalizes traditional spectral methods to completely general node layouts. Interpolants based on the new radial functions appear immune to many or possibly all cases of divergence that in this limit can arise with other standard types of radial functions (such as multiquadrics and inverse multiquadratics).

Original languageEnglish
Pages (from-to)1209-1222
Number of pages14
JournalComputers and Mathematics with Applications
Volume51
Issue number8 SPEC. ISS.
DOIs
StatePublished - Apr 2006

Keywords

  • Bessel functions
  • Multivariate interpolation
  • Radial basis functions
  • RBF

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