The error bounds of Gauss quadrature formulae for the modified weight functions of Chebyshev type
Само за регистроване кориснике
2020
Чланак у часопису (Објављена верзија)
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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.
Кључне речи:
remainder term for analytic functions / Gauss quadrature formulae / error bound / contour integral representation / Chebyshev weight functionsИзвор:
Applied Mathematics and Computation, 2020, 369Издавач:
- Elsevier Science Inc, New York
Финансирање / пројекти:
- Research Project of Ministerio de Ciencia e Innovacion (Spain) [MTM2015-71352-P
- Методе нумеричке и нелинеарне анализе са применама (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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Институција/група
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 . .