The error bounds of Gauss quadrature formulae for the modified weight functions of Chebyshev type
Abstract
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.
Keywords:
remainder term for analytic functions / Gauss quadrature formulae / error bound / contour integral representation / Chebyshev weight functionsSource:
Applied Mathematics and Computation, 2020, 369Publisher:
- Elsevier Science Inc, New York
Funding / projects:
- Research Project of Ministerio de Ciencia e Innovacion (Spain) [MTM2015-71352-P
- Methods of Numerical and Nonlinear Analysis with Applications (RS-MESTD-Basic Research (BR or ON)-174002)
DOI: 10.1016/j.amc.2019.124806
ISSN: 0096-3003
WoS: 000500918200045
Scopus: 2-s2.0-85074176919
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Institution/Community
Mašinski fakultetTY - JOUR AU - Orive, Ramon AU - Pejčev, Aleksandar AU - Spalević, Miodrag PY - 2020 UR - https://machinery.mas.bg.ac.rs/handle/123456789/3401 AB - 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. PB - Elsevier Science Inc, New York T2 - Applied Mathematics and Computation T1 - The error bounds of Gauss quadrature formulae for the modified weight functions of Chebyshev type VL - 369 DO - 10.1016/j.amc.2019.124806 ER -
@article{ author = "Orive, Ramon and Pejčev, Aleksandar and Spalević, Miodrag", year = "2020", abstract = "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.", publisher = "Elsevier Science Inc, New York", journal = "Applied Mathematics and Computation", title = "The error bounds of Gauss quadrature formulae for the modified weight functions of Chebyshev type", volume = "369", doi = "10.1016/j.amc.2019.124806" }
Orive, R., Pejčev, A.,& Spalević, M.. (2020). The error bounds of Gauss quadrature formulae for the modified weight functions of Chebyshev type. in Applied Mathematics and Computation Elsevier Science Inc, New York., 369. https://doi.org/10.1016/j.amc.2019.124806
Orive R, Pejčev A, Spalević M. The error bounds of Gauss quadrature formulae for the modified weight functions of Chebyshev type. in Applied Mathematics and Computation. 2020;369. doi:10.1016/j.amc.2019.124806 .
Orive, Ramon, Pejčev, Aleksandar, Spalević, Miodrag, "The error bounds of Gauss quadrature formulae for the modified weight functions of Chebyshev type" in Applied Mathematics and Computation, 369 (2020), https://doi.org/10.1016/j.amc.2019.124806 . .