Publikation: Generalized eigenvalue methods for Gaussian quadrature rules
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2020
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Annales Henri Lebesgue. École Normale Supérieure de Rennes (ENS Rennes). 2020, 3, pp. 1327-1341. eISSN 2644-9463. Available under: doi: 10.5802/ahl.62
Zusammenfassung
A quadrature rule μ of a measure on the real line represents a conic combination of finitely many evaluations at points, called nodes, that agrees with integration against 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.
Zusammenfassung in einer weiteren Sprache
Fachgebiet (DDC)
510 Mathematik
Schlagwörter
quadrature, Gaussian quadrature, plane curves
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BLEKHERMAN, Grigoriy, Mario KUMMER, Cordian RIENER, Markus SCHWEIGHOFER, Cynthia VINZANT, 2020. Generalized eigenvalue methods for Gaussian quadrature rules. In: Annales Henri Lebesgue. École Normale Supérieure de Rennes (ENS Rennes). 2020, 3, pp. 1327-1341. eISSN 2644-9463. Available under: doi: 10.5802/ahl.62BibTex
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year={2020},
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title={Generalized eigenvalue methods for Gaussian quadrature rules},
volume={3},
journal={Annales Henri Lebesgue},
pages={1327--1341},
author={Blekherman, Grigoriy and Kummer, Mario and Riener, Cordian and Schweighofer, Markus and Vinzant, Cynthia}
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