Kernel-based interpolation at approximate Fekete points

Toni Karvonen*, Simo Särkkä, Ken’ichiro Tanaka

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

Abstract

We construct approximate Fekete point sets for kernel-based interpolation by maximising the determinant of a kernel Gram matrix obtained via truncation of an orthonormal expansion of the kernel. Uniform error estimates are proved for kernel interpolants at the resulting points. If the kernel is Gaussian, we show that the approximate Fekete points in one dimension are the solution to a convex optimisation problem and that the interpolants converge with a super-exponential rate. Numerical examples are provided for the Gaussian kernel.

Original languageEnglish
Number of pages24
JournalNUMERICAL ALGORITHMS
DOIs
Publication statusPublished - 10 Jul 2020
MoE publication typeA1 Journal article-refereed

Keywords

  • Gaussian kernel
  • Radial basis functions
  • Reproducing kernel Hilbert spaces

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