Gaussian kernel quadrature at scaled Gauss–Hermite nodes

Research output: Contribution to journalArticleScientificpeer-review

Researchers

Research units

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.

Details

Original languageEnglish
Number of pages26
JournalBIT - Numerical Mathematics
Publication statusPublished - 2019
MoE publication typeA1 Journal article-refereed

    Research areas

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

Download statistics

No data available

ID: 33799135