Numerical integration as a finite matrix approximation to multiplication operator

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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.

Yksityiskohdat

AlkuperäiskieliEnglanti
Sivut283-291
Sivumäärä9
JulkaisuJournal of Computational and Applied Mathematics
Vuosikerta353
TilaJulkaistu - 1 kesäkuuta 2019
OKM-julkaisutyyppiA1 Julkaistu artikkeli, soviteltu

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