C<sup>∞</sup> compactly supported and positive definite radial kernels

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

A family of C<sup>∞</sup> 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<sup>∞</sup> 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 - 2015

Fingerprint

Positive definite
kernel
Radial Functions
Positive Definite Kernels
Convolution
Basis Functions
Smoothness
Numerical Experiment
Alternatives
Approximation
Demonstrate
Experiments
Family

Keywords

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

ASJC Scopus subject areas

  • Applied Mathematics
  • Computational Mathematics

Cite this

C<sup>∞</sup> compactly supported and positive definite radial kernels. / Platte, Rodrigo.

In: SIAM Journal on Scientific Computing, Vol. 37, No. 4, 2015, p. A1934-A1956.

Research output: Contribution to journalArticle

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