On the remainder term of Gauss-Radau quadrature with Chebyshev weight of the third kind for analytic functions
Само за регистроване кориснике
2012
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For analytic functions the remainder term 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 and a sum of semi-axes rho > 1, for Gauss-Radau quadrature formula with Chebyshev weight function of the third kind. Starting from the explicit expression of the corresponding kernel, derived by Gautschi, 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 in his paper [W. Gautschi, On the remainder term for analytic functions of Gauss-Lobatto and Gauss-Radau quadratures, Rocky Mounatin J. Math. 21 (1991) 209-206]. In this way the last unproved conjecture from the mentioned paper is now verified.
Кључне речи:
Remainder term for analytic functions / Gauss-Radau quadrature formula / Error bound / Contour integral representation / Chebyshev weight functionИзвор:
Applied Mathematics and Computation, 2012, 219, 5, 2760-2765Издавач:
- Elsevier Science Inc, New York
Финансирање / пројекти:
- Методе нумеричке и нелинеарне анализе са применама (RS-MESTD-Basic Research (BR or ON)-174002)
DOI: 10.1016/j.amc.2012.09.002
ISSN: 0096-3003
WoS: 000310504500034
Scopus: 2-s2.0-84868211525
Колекције
Институција/група
Mašinski fakultetTY - JOUR AU - Pejčev, Aleksandar AU - Spalević, Miodrag PY - 2012 UR - https://machinery.mas.bg.ac.rs/handle/123456789/1522 AB - For analytic functions the remainder term 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 and a sum of semi-axes rho > 1, for Gauss-Radau quadrature formula with Chebyshev weight function of the third kind. Starting from the explicit expression of the corresponding kernel, derived by Gautschi, 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 in his paper [W. Gautschi, On the remainder term for analytic functions of Gauss-Lobatto and Gauss-Radau quadratures, Rocky Mounatin J. Math. 21 (1991) 209-206]. In this way the last unproved conjecture from the mentioned paper is now verified. PB - Elsevier Science Inc, New York T2 - Applied Mathematics and Computation T1 - On the remainder term of Gauss-Radau quadrature with Chebyshev weight of the third kind for analytic functions EP - 2765 IS - 5 SP - 2760 VL - 219 DO - 10.1016/j.amc.2012.09.002 ER -
@article{ author = "Pejčev, Aleksandar and Spalević, Miodrag", year = "2012", abstract = "For analytic functions the remainder term 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 and a sum of semi-axes rho > 1, for Gauss-Radau quadrature formula with Chebyshev weight function of the third kind. Starting from the explicit expression of the corresponding kernel, derived by Gautschi, 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 in his paper [W. Gautschi, On the remainder term for analytic functions of Gauss-Lobatto and Gauss-Radau quadratures, Rocky Mounatin J. Math. 21 (1991) 209-206]. In this way the last unproved conjecture from the mentioned paper is now verified.", publisher = "Elsevier Science Inc, New York", journal = "Applied Mathematics and Computation", title = "On the remainder term of Gauss-Radau quadrature with Chebyshev weight of the third kind for analytic functions", pages = "2765-2760", number = "5", volume = "219", doi = "10.1016/j.amc.2012.09.002" }
Pejčev, A.,& Spalević, M.. (2012). On the remainder term of Gauss-Radau quadrature with Chebyshev weight of the third kind for analytic functions. in Applied Mathematics and Computation Elsevier Science Inc, New York., 219(5), 2760-2765. https://doi.org/10.1016/j.amc.2012.09.002
Pejčev A, Spalević M. On the remainder term of Gauss-Radau quadrature with Chebyshev weight of the third kind for analytic functions. in Applied Mathematics and Computation. 2012;219(5):2760-2765. doi:10.1016/j.amc.2012.09.002 .
Pejčev, Aleksandar, Spalević, Miodrag, "On the remainder term of Gauss-Radau quadrature with Chebyshev weight of the third kind for analytic functions" in Applied Mathematics and Computation, 219, no. 5 (2012):2760-2765, https://doi.org/10.1016/j.amc.2012.09.002 . .