Error Bounds for Gauss-Lobatto Quadrature Formula with Multiple End Points with Chebyshev Weight Function of the Third and the Fourth Kind
Апстракт
For analytic functions the remainder terms of quadrature formulae can be represented as a contour integral with a complex kernel. We study the kernel, on elliptic contours with foci at the points -/+ 1, for Gauss-Lobatto quadrature formula with multiple end points with Chebyshev weight function of the third and the fourth kind. Starting from the explicit expression of the corresponding kernel, derived by Gautschi and Li, we determine the locations on the ellipses where maximum modulus of the kernel is attained. The obtained values confirm the corresponding conjectured values given by Gautschi and Li in paper [The remainder term for analytic functions of Gauss-Radau and Gauss-Lobatto quadrature rules with multiple end points, Journal of Computational and Applied Mathematics 33 (1990) 315-329.]
Кључне речи:
remainder term for analytic functions / Gauss-Lobatto quadrature formula / error bound / contour integral representation / Chebyshev weight functionИзвор:
Filomat, 2016, 30, 1, 231-239Издавач:
- Univerzitet u Nišu - Prirodno-matematički fakultet - Departmant za matematiku i informatiku, Niš
Финансирање / пројекти:
- Методе нумеричке и нелинеарне анализе са применама (RS-MESTD-Basic Research (BR or ON)-174002)
DOI: 10.2298/FIL1601231M
ISSN: 0354-5180
WoS: 000376533000021
Scopus: 2-s2.0-84966687568
Колекције
Институција/група
Mašinski fakultetTY - JOUR AU - Mihić, Ljubica AU - Pejčev, Aleksandar AU - Spalević, Miodrag PY - 2016 UR - https://machinery.mas.bg.ac.rs/handle/123456789/2281 AB - For analytic functions the remainder terms of quadrature formulae can be represented as a contour integral with a complex kernel. We study the kernel, on elliptic contours with foci at the points -/+ 1, for Gauss-Lobatto quadrature formula with multiple end points with Chebyshev weight function of the third and the fourth kind. Starting from the explicit expression of the corresponding kernel, derived by Gautschi and Li, we determine the locations on the ellipses where maximum modulus of the kernel is attained. The obtained values confirm the corresponding conjectured values given by Gautschi and Li in paper [The remainder term for analytic functions of Gauss-Radau and Gauss-Lobatto quadrature rules with multiple end points, Journal of Computational and Applied Mathematics 33 (1990) 315-329.] PB - Univerzitet u Nišu - Prirodno-matematički fakultet - Departmant za matematiku i informatiku, Niš T2 - Filomat T1 - Error Bounds for Gauss-Lobatto Quadrature Formula with Multiple End Points with Chebyshev Weight Function of the Third and the Fourth Kind EP - 239 IS - 1 SP - 231 VL - 30 DO - 10.2298/FIL1601231M ER -
@article{ author = "Mihić, Ljubica and Pejčev, Aleksandar and Spalević, Miodrag", year = "2016", abstract = "For analytic functions the remainder terms of quadrature formulae can be represented as a contour integral with a complex kernel. We study the kernel, on elliptic contours with foci at the points -/+ 1, for Gauss-Lobatto quadrature formula with multiple end points with Chebyshev weight function of the third and the fourth kind. Starting from the explicit expression of the corresponding kernel, derived by Gautschi and Li, we determine the locations on the ellipses where maximum modulus of the kernel is attained. The obtained values confirm the corresponding conjectured values given by Gautschi and Li in paper [The remainder term for analytic functions of Gauss-Radau and Gauss-Lobatto quadrature rules with multiple end points, Journal of Computational and Applied Mathematics 33 (1990) 315-329.]", publisher = "Univerzitet u Nišu - Prirodno-matematički fakultet - Departmant za matematiku i informatiku, Niš", journal = "Filomat", title = "Error Bounds for Gauss-Lobatto Quadrature Formula with Multiple End Points with Chebyshev Weight Function of the Third and the Fourth Kind", pages = "239-231", number = "1", volume = "30", doi = "10.2298/FIL1601231M" }
Mihić, L., Pejčev, A.,& Spalević, M.. (2016). Error Bounds for Gauss-Lobatto Quadrature Formula with Multiple End Points with Chebyshev Weight Function of the Third and the Fourth Kind. in Filomat Univerzitet u Nišu - Prirodno-matematički fakultet - Departmant za matematiku i informatiku, Niš., 30(1), 231-239. https://doi.org/10.2298/FIL1601231M
Mihić L, Pejčev A, Spalević M. Error Bounds for Gauss-Lobatto Quadrature Formula with Multiple End Points with Chebyshev Weight Function of the Third and the Fourth Kind. in Filomat. 2016;30(1):231-239. doi:10.2298/FIL1601231M .
Mihić, Ljubica, Pejčev, Aleksandar, Spalević, Miodrag, "Error Bounds for Gauss-Lobatto Quadrature Formula with Multiple End Points with Chebyshev Weight Function of the Third and the Fourth Kind" in Filomat, 30, no. 1 (2016):231-239, https://doi.org/10.2298/FIL1601231M . .