Journal
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
Volume 284, Issue -, Pages 235-243Publisher
ELSEVIER SCIENCE BV
DOI: 10.1016/j.cam.2014.11.016
Keywords
Gauss quadrature; Anti-Gauss quadrature; Error estimate
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Funding
- Serbian Ministry of Education and Science [174002]
- NSF [DMS-1115385]
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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 n-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 n-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 n-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. (C) 2014 Elsevier B.V. All rights reserved.
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