Numerical integration as a finite matrix approximation to multiplication operator

Juha Sarmavuori*, Simo Särkkä

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

1 Citation (Scopus)

Abstract

In this article, numerical integration is formulated as evaluation of a matrix function of a matrix that is obtained as a projection of the multiplication operator on a finite-dimensional basis. The idea is to approximate the continuous spectral representation of a multiplication operator on a Hilbert space with a discrete spectral representation of a Hermitian matrix. The Gaussian quadrature is shown to be a special case of the new method. The placement of the nodes of numerical integration and convergence of the new method are studied.

Original languageEnglish
Pages (from-to)283-291
Number of pages9
JournalJournal of Computational and Applied Mathematics
Volume353
DOIs
Publication statusPublished - 1 Jun 2019
MoE publication typeA1 Journal article-refereed

Keywords

  • Gaussian quadrature
  • Matrix function
  • Multiplication operator
  • Numerical integration

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