Generalized anti-Gauss quadrature rules
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Miroslav S. Pranić [1] ; Lothar Reichel [2]
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[1] University of Banja Luka
University of Banja Luka
Bosnia y Herzegovina
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[2] Kent State University
Kent State University
City of Kent, Estados Unidos
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- Localización: Journal of computational and applied mathematics, ISSN 0377-0427, Vol. 284, Nº 1 (15 August 2015), 2015, págs. 235-243
- Idioma: inglés
- DOI: 10.1016/j.cam.2014.11.016
- Enlaces
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Resumen
Gauss quadrature is a popular approach to approximate the value of a desired integral determined by a measure with support on the real axis. Laurie proposed an (n+1)-point quadrature rule that gives an error of the same magnitude and of opposite sign as the associated nn-point Gauss quadrature rule for all polynomials of degree up to 2n+1. This rule is referred to as an anti-Gauss rule. It is useful for the estimation of the error in the approximation of the desired integral furnished by the nn-point Gauss rule. This paper describes a modification of the (n+1)-point anti-Gauss rule, that has n+k nodes and gives an error of the same magnitude and of opposite sign as the associated nn-point Gauss quadrature rule for all polynomials of degree up to 2n+2k−1 for some k>1. We refer to this rule as a generalized anti-Gauss rule. An application to error estimation of matrix functionals is presented.
