On the Gauss-Kronrod quadrature formula for a modified weight function of Chebyshev type
Apstrakt
In this paper, we consider the Gauss-Kronrod quadrature formulas for a modified Chebyshev weight. Efficient estimates of the error of these Gauss-Kronrod formulae for analytic functions are obtained, using techniques of contour integration that were introduced by Gautschi and Varga (cf. Gautschi and Varga SIAM J. Numer. Anal. 20, 1170-1186 1983). Some illustrative numerical examples which show both the accuracy of the Gauss-Kronrod formulas and the sharpness of our estimations are displayed. Though for the sake of brevity we restrict ourselves to the first kind Chebyshev weight, a similar analysis may be carried out for the other three Chebyshev type weights; part of the corresponding computations are included in a final appendix.
Ključne reči:
Remainder term for analytic functions / Gauss-Kronrod quadrature formulae / Error bound / Contour integral representation / Chebyshev weight functionIzvor:
Numerical Algorithms, 2022Izdavač:
- Springer, Dordrecht
Finansiranje / projekti:
- CRUE-CSIC agreement
- Springer Nature
- Ministarstvo nauke, tehnološkog razvoja i inovacija Republike Srbije, institucionalno finansiranje - 200105 (Univerzitet u Beogradu, Mašinski fakultet) (RS-MESTD-inst-2020-200105)
- Spanish Ministerio de Ciencia, Innovacion y Universidades [MTM2015-71352-P]
- Spanish Ministerio de Ciencia e Innovacion [PID2021-123367NB-100]
DOI: 10.1007/s11075-022-01325-8
ISSN: 1017-1398
WoS: 000805732200001
Scopus: 2-s2.0-85131520358
Kolekcije
Institucija/grupa
Mašinski fakultetTY - JOUR AU - Orive, Ramon AU - Pejčev, Aleksandar AU - Spalević, Miodrag AU - Mihić, Ljubica PY - 2022 UR - https://machinery.mas.bg.ac.rs/handle/123456789/88 AB - In this paper, we consider the Gauss-Kronrod quadrature formulas for a modified Chebyshev weight. Efficient estimates of the error of these Gauss-Kronrod formulae for analytic functions are obtained, using techniques of contour integration that were introduced by Gautschi and Varga (cf. Gautschi and Varga SIAM J. Numer. Anal. 20, 1170-1186 1983). Some illustrative numerical examples which show both the accuracy of the Gauss-Kronrod formulas and the sharpness of our estimations are displayed. Though for the sake of brevity we restrict ourselves to the first kind Chebyshev weight, a similar analysis may be carried out for the other three Chebyshev type weights; part of the corresponding computations are included in a final appendix. PB - Springer, Dordrecht T2 - Numerical Algorithms T1 - On the Gauss-Kronrod quadrature formula for a modified weight function of Chebyshev type DO - 10.1007/s11075-022-01325-8 ER -
@article{ author = "Orive, Ramon and Pejčev, Aleksandar and Spalević, Miodrag and Mihić, Ljubica", year = "2022", abstract = "In this paper, we consider the Gauss-Kronrod quadrature formulas for a modified Chebyshev weight. Efficient estimates of the error of these Gauss-Kronrod formulae for analytic functions are obtained, using techniques of contour integration that were introduced by Gautschi and Varga (cf. Gautschi and Varga SIAM J. Numer. Anal. 20, 1170-1186 1983). Some illustrative numerical examples which show both the accuracy of the Gauss-Kronrod formulas and the sharpness of our estimations are displayed. Though for the sake of brevity we restrict ourselves to the first kind Chebyshev weight, a similar analysis may be carried out for the other three Chebyshev type weights; part of the corresponding computations are included in a final appendix.", publisher = "Springer, Dordrecht", journal = "Numerical Algorithms", title = "On the Gauss-Kronrod quadrature formula for a modified weight function of Chebyshev type", doi = "10.1007/s11075-022-01325-8" }
Orive, R., Pejčev, A., Spalević, M.,& Mihić, L.. (2022). On the Gauss-Kronrod quadrature formula for a modified weight function of Chebyshev type. in Numerical Algorithms Springer, Dordrecht.. https://doi.org/10.1007/s11075-022-01325-8
Orive R, Pejčev A, Spalević M, Mihić L. On the Gauss-Kronrod quadrature formula for a modified weight function of Chebyshev type. in Numerical Algorithms. 2022;. doi:10.1007/s11075-022-01325-8 .
Orive, Ramon, Pejčev, Aleksandar, Spalević, Miodrag, Mihić, Ljubica, "On the Gauss-Kronrod quadrature formula for a modified weight function of Chebyshev type" in Numerical Algorithms (2022), https://doi.org/10.1007/s11075-022-01325-8 . .