Gaussian kernel quadrature at scaled Gauss–Hermite nodes

Toni Karvonen, Simo Särkkä

Research output: Contribution to journalArticleScientificpeer-review

5 Citations (Scopus)
92 Downloads (Pure)

Abstract

This article derives an accurate, explicit, and numerically stable approximation to the kernel quadrature weights in one dimension and on tensor product grids when the kernel and integration measure are Gaussian. The approximation is based on use of scaled Gauss–Hermite nodes and truncation of the Mercer eigendecomposition of the Gaussian kernel. Numerical evidence indicates that both the kernel quadrature and the approximate weights at these nodes are positive. An exponential rate of convergence for functions in the reproducing kernel Hilbert space induced by the Gaussian kernel is proved under an assumption on growth of the sum of absolute values of the approximate weights.
Original languageEnglish
Pages (from-to)877–902
Number of pages26
JournalBIT - Numerical Mathematics
DOIs
Publication statusPublished - 2019
MoE publication typeA1 Journal article-refereed

Keywords

  • Numerical integration
  • Kernel quadrature
  • Gaussian quadrature
  • Mercer eigendecomposition

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