Maximum of the modulus of kernels in Gauss-Turan quadratures
Само за регистроване кориснике
2008
Чланак у часопису (Објављена верзија)
Метаподаци
Приказ свих података о документуАпстракт
We study the kernels
in the remainder terms
of the Gauss-Turán quadrature formulae for analytic functions on elliptical contours with foci at , when the weight
is a generalized Chebyshev weight function. For the generalized Chebyshev weight of the first (third) kind, it is shown that the modulus of the kernel
attains its maximum on the real axis (positive real semi-axis) for each
. It was stated as a conjecture in [Math. Comp. 72 (2003), 1855–1872]. For the generalized Chebyshev weight of the second kind, in the case when the number of the nodes
in the corresponding Gauss-Turán quadrature formula is even, it is shown that the modulus of the kernel attains its maximum on the imaginary axis for each
. Numerical examples are included.
Кључне речи:
Gauss-Turan quadrature / Chebyshev weight functions / remainder term for analytic functions / error estimate / contour integral representation / confocal ellipses / kernelИзвор:
Mathematics of Computation, 2008, 77, 262, 985-994Издавач:
- American Mathematical Society
Финансирање / пројекти:
- Serbian Ministry of Science and Environmental Protection (Project #144005A: “Approximation of linear operators”)
Институција/група
Mašinski fakultetTY - JOUR AU - Milovanović, Gradimir AU - Spalević, Miodrag AU - Pranić, Miroslav PY - 2008 UR - https://machinery.mas.bg.ac.rs/handle/123456789/5087 AB - We study the kernels in the remainder terms of the Gauss-Turán quadrature formulae for analytic functions on elliptical contours with foci at , when the weight is a generalized Chebyshev weight function. For the generalized Chebyshev weight of the first (third) kind, it is shown that the modulus of the kernel attains its maximum on the real axis (positive real semi-axis) for each . It was stated as a conjecture in [Math. Comp. 72 (2003), 1855–1872]. For the generalized Chebyshev weight of the second kind, in the case when the number of the nodes in the corresponding Gauss-Turán quadrature formula is even, it is shown that the modulus of the kernel attains its maximum on the imaginary axis for each . Numerical examples are included. PB - American Mathematical Society T2 - Mathematics of Computation T1 - Maximum of the modulus of kernels in Gauss-Turan quadratures EP - 994 IS - 262 SP - 985 VL - 77 UR - https://hdl.handle.net/21.15107/rcub_machinery_5087 ER -
@article{ author = "Milovanović, Gradimir and Spalević, Miodrag and Pranić, Miroslav", year = "2008", abstract = "We study the kernels in the remainder terms of the Gauss-Turán quadrature formulae for analytic functions on elliptical contours with foci at , when the weight is a generalized Chebyshev weight function. For the generalized Chebyshev weight of the first (third) kind, it is shown that the modulus of the kernel attains its maximum on the real axis (positive real semi-axis) for each . It was stated as a conjecture in [Math. Comp. 72 (2003), 1855–1872]. For the generalized Chebyshev weight of the second kind, in the case when the number of the nodes in the corresponding Gauss-Turán quadrature formula is even, it is shown that the modulus of the kernel attains its maximum on the imaginary axis for each . Numerical examples are included.", publisher = "American Mathematical Society", journal = "Mathematics of Computation", title = "Maximum of the modulus of kernels in Gauss-Turan quadratures", pages = "994-985", number = "262", volume = "77", url = "https://hdl.handle.net/21.15107/rcub_machinery_5087" }
Milovanović, G., Spalević, M.,& Pranić, M.. (2008). Maximum of the modulus of kernels in Gauss-Turan quadratures. in Mathematics of Computation American Mathematical Society., 77(262), 985-994. https://hdl.handle.net/21.15107/rcub_machinery_5087
Milovanović G, Spalević M, Pranić M. Maximum of the modulus of kernels in Gauss-Turan quadratures. in Mathematics of Computation. 2008;77(262):985-994. https://hdl.handle.net/21.15107/rcub_machinery_5087 .
Milovanović, Gradimir, Spalević, Miodrag, Pranić, Miroslav, "Maximum of the modulus of kernels in Gauss-Turan quadratures" in Mathematics of Computation, 77, no. 262 (2008):985-994, https://hdl.handle.net/21.15107/rcub_machinery_5087 .