Numerical integration as a finite matrix approximation to multiplication operator
Research output: Contribution to journal › Article › Scientific › peer-review
|Number of pages||9|
|Journal||Journal of Computational and Applied Mathematics|
|Publication status||Published - 1 Jun 2019|
|MoE publication type||A1 Journal article-refereed|
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.
- Gaussian quadrature, Matrix function, Multiplication operator, Numerical integration