C compactly supported and positive definite radial kernels

Research output: Contribution to journalReview article

2 Scopus citations

Abstract

A family of C compactly supported radial kernels is presented. These positive definite kernels can be generated numerically using convolutions of compactly supported radial functions. An alternative proof that shows the infinitely smooth limit of the well-known Wendland functions is not a suitable C compactly supported kernel is also presented. Numerical experiments are provided to demonstrate the accuracy of approximations of the proposed kernels, including comparisons with Gaussians and Wendland radial basis functions of finite smoothness.

Original languageEnglish (US)
Pages (from-to)A1934-A1956
JournalSIAM Journal on Scientific Computing
Volume37
Issue number4
DOIs
StatePublished - Jan 1 2015

Keywords

  • Infinitely smooth kernels
  • Meshfree approximation
  • Radial basis functions
  • Scattered data
  • Wendland functions

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics

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