Error bound of Gaussian quadrature rules for certain Gegenbauer weight functions
Само за регистроване кориснике
2024
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In this paper we present an extension of our previous research, focusing on a method to numerically evaluate the error term in the Gaussian quadrature formula with the Legendre weight function, as discussed by Jandrlic et al. (2022). For an analytic integrand, the error term in Gaussian quadrature can be expressed as a contour integral. Consequently, determining the upper bound of the error term involves identifying the maximum value of the modulus of the kernel within the subintegral expression for the error along this contour. In our previous study, we investigated the position of this maximum point on the ellipse for Legendre polynomials. In this paper, we establish sufficient conditions for the maximum of the modulus of the kernel, which we derived analytically, to occur at one of the semi-axes for Gegenbauer polynomials. This result extends to a significantly broader case. We present an effective error estimation that we compare with the actual one. Some numerical results are pres...ented.
Кључне речи:
Gauss quadrature formulae / Gegenbauer polynomials / Remainder term for analytic function / Error boundИзвор:
Journal of Computational and Applied Mathematics, 2024, 440, Art. 115586Издавач:
- Elsevier
Финансирање / пројекти:
- nfo:eu-repo/grantAgreement/MESTD/inst-2020/200105/RS//
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Институција/група
Mašinski fakultetTY - JOUR AU - Jandrlić, Davorka AU - Pejčev, Aleksandar AU - Spalević, Miodrag PY - 2024 UR - https://machinery.mas.bg.ac.rs/handle/123456789/7069 AB - In this paper we present an extension of our previous research, focusing on a method to numerically evaluate the error term in the Gaussian quadrature formula with the Legendre weight function, as discussed by Jandrlic et al. (2022). For an analytic integrand, the error term in Gaussian quadrature can be expressed as a contour integral. Consequently, determining the upper bound of the error term involves identifying the maximum value of the modulus of the kernel within the subintegral expression for the error along this contour. In our previous study, we investigated the position of this maximum point on the ellipse for Legendre polynomials. In this paper, we establish sufficient conditions for the maximum of the modulus of the kernel, which we derived analytically, to occur at one of the semi-axes for Gegenbauer polynomials. This result extends to a significantly broader case. We present an effective error estimation that we compare with the actual one. Some numerical results are presented. PB - Elsevier T2 - Journal of Computational and Applied Mathematics T1 - Error bound of Gaussian quadrature rules for certain Gegenbauer weight functions IS - Art. 115586 VL - 440 DO - 10.1016/j.cam.2023.115661 ER -
@article{ author = "Jandrlić, Davorka and Pejčev, Aleksandar and Spalević, Miodrag", year = "2024", abstract = "In this paper we present an extension of our previous research, focusing on a method to numerically evaluate the error term in the Gaussian quadrature formula with the Legendre weight function, as discussed by Jandrlic et al. (2022). For an analytic integrand, the error term in Gaussian quadrature can be expressed as a contour integral. Consequently, determining the upper bound of the error term involves identifying the maximum value of the modulus of the kernel within the subintegral expression for the error along this contour. In our previous study, we investigated the position of this maximum point on the ellipse for Legendre polynomials. In this paper, we establish sufficient conditions for the maximum of the modulus of the kernel, which we derived analytically, to occur at one of the semi-axes for Gegenbauer polynomials. This result extends to a significantly broader case. We present an effective error estimation that we compare with the actual one. Some numerical results are presented.", publisher = "Elsevier", journal = "Journal of Computational and Applied Mathematics", title = "Error bound of Gaussian quadrature rules for certain Gegenbauer weight functions", number = "Art. 115586", volume = "440", doi = "10.1016/j.cam.2023.115661" }
Jandrlić, D., Pejčev, A.,& Spalević, M.. (2024). Error bound of Gaussian quadrature rules for certain Gegenbauer weight functions. in Journal of Computational and Applied Mathematics Elsevier., 440(Art. 115586). https://doi.org/10.1016/j.cam.2023.115661
Jandrlić D, Pejčev A, Spalević M. Error bound of Gaussian quadrature rules for certain Gegenbauer weight functions. in Journal of Computational and Applied Mathematics. 2024;440(Art. 115586). doi:10.1016/j.cam.2023.115661 .
Jandrlić, Davorka, Pejčev, Aleksandar, Spalević, Miodrag, "Error bound of Gaussian quadrature rules for certain Gegenbauer weight functions" in Journal of Computational and Applied Mathematics, 440, no. Art. 115586 (2024), https://doi.org/10.1016/j.cam.2023.115661 . .