Numerical integration as a finite matrix approximation to multiplication operator

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:353

Article

Sarmavuori, Juha¹  Sarkka, Simo¹ 

[1] Aalto Univ, Dept Elect Engn & Automat, POB 12200, FI-00076 Aalto, Finland

关键词: Numerical integration;    Multiplication operator;    Matrix function;    Gaussian quadrature;   

DOI  :  10.1016/j.cam.2018.12.031

来源: Elsevier

【 摘 要 】

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. (C) 2018 Elsevier B.V. All rights reserved.

【 授权许可】

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