Starting from the explicit expression of the corresponding kernels, derived by Gautschi and Li (W. Gautschi, S. Li: The remainder term for analytic functions of Gauss-Lobatto and Gauss-Radau quadrature rules with multiple end points, J. Comput. Appl. Math. 33 (1990) 315-329), we determine the exact dimensions of the minimal ellipses on which the modulus of the kernel starts to behave in the described way. The effective error bounds for Gauss-Radau and Gauss-Lobatto quadrature formulas with double end point(s) are derived. The comparisons are made with the actual errors.
Keywords:
Gauss-Radau and Gauss-Lobatto quadratures / Error bounds / Chebyshev weight function
Source:
Applicable Analysis and Discrete Mathematics, 2019, 13, 2, 463-477
Publisher:
Univerzitet u Beogradu - Elektrotehnički fakultet, Beograd i Akademska misao, Beograd
TY - JOUR
AU - Pejčev, Aleksandar
AU - Mihić, Ljubica
PY - 2019
UR - https://machinery.mas.bg.ac.rs/handle/123456789/3115
AB - Starting from the explicit expression of the corresponding kernels, derived by Gautschi and Li (W. Gautschi, S. Li: The remainder term for analytic functions of Gauss-Lobatto and Gauss-Radau quadrature rules with multiple end points, J. Comput. Appl. Math. 33 (1990) 315-329), we determine the exact dimensions of the minimal ellipses on which the modulus of the kernel starts to behave in the described way. The effective error bounds for Gauss-Radau and Gauss-Lobatto quadrature formulas with double end point(s) are derived. The comparisons are made with the actual errors.
PB - Univerzitet u Beogradu - Elektrotehnički fakultet, Beograd i Akademska misao, Beograd
T2 - Applicable Analysis and Discrete Mathematics
T1 - Errors of gauss-radau and gauss-lobatto quadratures with double end point
EP - 477
IS - 2
SP - 463
VL - 13
DO - 10.2298/AADM180408011P
ER -
@article{
author = "Pejčev, Aleksandar and Mihić, Ljubica",
year = "2019",
abstract = "Starting from the explicit expression of the corresponding kernels, derived by Gautschi and Li (W. Gautschi, S. Li: The remainder term for analytic functions of Gauss-Lobatto and Gauss-Radau quadrature rules with multiple end points, J. Comput. Appl. Math. 33 (1990) 315-329), we determine the exact dimensions of the minimal ellipses on which the modulus of the kernel starts to behave in the described way. The effective error bounds for Gauss-Radau and Gauss-Lobatto quadrature formulas with double end point(s) are derived. The comparisons are made with the actual errors.",
publisher = "Univerzitet u Beogradu - Elektrotehnički fakultet, Beograd i Akademska misao, Beograd",
journal = "Applicable Analysis and Discrete Mathematics",
title = "Errors of gauss-radau and gauss-lobatto quadratures with double end point",
pages = "477-463",
number = "2",
volume = "13",
doi = "10.2298/AADM180408011P"
}
Pejčev, A.,& Mihić, L.. (2019). Errors of gauss-radau and gauss-lobatto quadratures with double end point. in Applicable Analysis and Discrete Mathematics
Univerzitet u Beogradu - Elektrotehnički fakultet, Beograd i Akademska misao, Beograd., 13(2), 463-477.
https://doi.org/10.2298/AADM180408011P
Pejčev A, Mihić L. Errors of gauss-radau and gauss-lobatto quadratures with double end point. in Applicable Analysis and Discrete Mathematics. 2019;13(2):463-477.
doi:10.2298/AADM180408011P .
Pejčev, Aleksandar, Mihić, Ljubica, "Errors of gauss-radau and gauss-lobatto quadratures with double end point" in Applicable Analysis and Discrete Mathematics, 13, no. 2 (2019):463-477,
https://doi.org/10.2298/AADM180408011P . .
