TY - JOUR
T1 - Numerical integration as a finite matrix approximation to multiplication operator
AU - Sarmavuori, Juha
AU - Särkkä, Simo
PY - 2019/6/1
Y1 - 2019/6/1
N2 - 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.
AB - 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.
KW - Gaussian quadrature
KW - Matrix function
KW - Multiplication operator
KW - Numerical integration
UR - http://www.scopus.com/inward/record.url?scp=85059867664&partnerID=8YFLogxK
U2 - 10.1016/j.cam.2018.12.031
DO - 10.1016/j.cam.2018.12.031
M3 - Article
AN - SCOPUS:85059867664
SN - 0377-0427
VL - 353
SP - 283
EP - 291
JO - Journal of Computational and Applied Mathematics
JF - Journal of Computational and Applied Mathematics
ER -