Some Observations Regarding Interpolants in the Limit of Flat Radial Basis Functions

B. Fornberg, G. Wright, E. Larsson

Research output: Contribution to journalArticlepeer-review

145 Scopus citations

Abstract

Radial basis functions (RBFs) form a primary tool for multivariate interpolation. Some of the most commonly used radial functions feature a shape parameter, allowing them to vary from being nearly flat (ε small) to sharply peaked (ε large). The former limit can be particularly accurate when interpolating a smooth function based on scattered data. This study discusses theoretical and computational aspects of the ε → 0 limit, and includes the conjecture that Gaussian RBF interpolants will never diverge in this limit.

Original languageEnglish
Pages (from-to)37-55
Number of pages19
JournalComputers and Mathematics with Applications
Volume47
Issue number1
DOIs
StatePublished - Jan 2004

Keywords

  • Multivariate interpolation
  • Radial basis functions (RBF)

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