Journal
APPLIED MATHEMATICS AND COMPUTATION
Volume 369, Issue -, Pages -Publisher
ELSEVIER SCIENCE INC
DOI: 10.1016/j.amc.2019.124806
Keywords
Gauss quadrature formulae; Chebyshev weight functions; contour integral representation; remainder term for analytic functions; error bound
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Funding
- Research Project of Ministerio de Ciencia e Innovacion (Spain) [MTM2015-71352-P]
- Serbian Ministry of Education, Science and Technological Development [174002]
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In this paper, we consider the Gauss quadrature formulae corresponding to some modifications of each of the four Chebyshev weights, considered by Gautschi and Li in [4]. As it is well known, in the case of analytic integrands the error of these quadrature formulas can be represented as a contour integral with a complex kernel. We study the kernel of the mentioned quadrature formulas on suitable elliptic contours, in such a way that the behavior of its modulus is analyzed in a rather simple manner, allowing us to derive some effective error bounds. In addition, some numerical examples checking the accuracy of such error bounds are included. (C) 2019 Elsevier Inc. All rights reserved.
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