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 |
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Pages (from-to) | 283-291 |
Number of pages | 9 |
Journal | Journal of Computational and Applied Mathematics |
Volume | 353 |
DOIs | |
Publication status | Published - 1 Jun 2019 |
MoE publication type | A1 Journal article-refereed |
Keywords
- Gaussian quadrature
- Matrix function
- Multiplication operator
- Numerical integration