Numerical integration as a finite matrix approximation to multiplication operator

Juha Sarmavuori; Simo Särkkä

doi:10.1016/j.cam.2018.12.031

Numerical integration as a finite matrix approximation to multiplication operator

Juha Sarmavuori^*, Simo Särkkä

^*Corresponding author for this work

Research output: Contribution to journal › Article › Scientific › peer-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 language	English
Pages (from-to)	283-291
Number of pages	9
Journal	Journal of Computational and Applied Mathematics
Volume	353
DOIs	https://doi.org/10.1016/j.cam.2018.12.031
Publication status	Published - 1 Jun 2019
MoE publication type	A1 Journal article-refereed

Keywords

Gaussian quadrature
Matrix function
Multiplication operator
Numerical integration

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Sarmavuori, J., & Särkkä, S. (2019). Numerical integration as a finite matrix approximation to multiplication operator. Journal of Computational and Applied Mathematics, 353, 283-291. https://doi.org/10.1016/j.cam.2018.12.031

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