Computing Gaussian quadrature rules with high relative accuracy.

Autor:	Laudadio, Teresa, Mastronardi, Nicola, Van Dooren, Paul
Předmět:	SINGULAR value decomposition MATRIX decomposition SYMMETRIC functions COMPUTATIONAL complexity INTERIOR-point methods
Zdroj:	Numerical Algorithms; Jan2023, Vol. 92 Issue 1, p767-793, 27p
Abstrakt:	The computation of n-point Gaussian quadrature rules for symmetric weight functions is considered in this paper. It is shown that the nodes and the weights of the Gaussian quadrature rule can be retrieved from the singular value decomposition of a bidiagonal matrix of size n/2. The proposed numerical method allows to compute the nodes with high relative accuracy and a computational complexity of O (n 2). We also describe an algorithm for computing the weights of a generic Gaussian quadrature rule with high relative accuracy. Numerical examples show the effectiveness of the proposed approach. [ABSTRACT FROM AUTHOR]
Databáze:	Complementary Index
Externí odkaz:	Zobrazit plný text záznamu Full text from SpringerLink