Generalized eigenvalue methods for Gaussian quadrature rules

Autor:	Blekherman, Grigoriy, Kummer, Mario, Riener, Cordian, Schweighofer, Markus, Vinzant, Cynthia
Rok vydání:	2018
Předmět:	Mathematics - Numerical Analysis Mathematics - Algebraic Geometry Primary 65D32 Secondary 14H50 14P05 15A22
Druh dokumentu:	Working Paper
DOI:	10.5802/ahl.62
Popis:	A quadrature rule of a measure $\mu$ on the real line represents a convex combination of finitely many evaluations at points, called nodes, that agrees with integration against $\mu$ for all polynomials up to some fixed degree. In this paper, we present a bivariate polynomial whose roots parametrize the nodes of minimal quadrature rules for measures on the real line. We give two symmetric determinantal formulas for this polynomial, which translate the problem of finding the nodes to solving a generalized eigenvalue problem. Comment: 13 pages, 2 figures
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1805.12047 Zobrazit plný text záznamu View this record from Arxiv