Monotonicity of the error term in Gauss-Turan quadratures for analytic functions
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2007
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For Gauss-Turan quadrature formulae with an even weight function on the interval [—1, 1] and functions analytic in regions of the complex plane which contain in their interiors a circle of radius greater than 1, the error term is investigated. In some particular cases we prove that the error decreases monotonically to zero. Also, for certain more general cases, we illustrate how to check numerically if this property holds. Some l^2-error estimates are considered.
Ključne reči:
Gauss-Turan quadrature / error term / monotonicity / weight function / analytic functionsIzvor:
ANZIAM Journal, 2007, 48, 567-581Izdavač:
- Cambridge University Press
Finansiranje / projekti:
- Serbian Ministry of Science and Environmental Protection (Project #144005A: “Approximation of linear operators”)
Institucija/grupa
Mašinski fakultetTY - JOUR AU - Milovanović, Gradimir AU - Spalević, Miodrag PY - 2007 UR - https://machinery.mas.bg.ac.rs/handle/123456789/5073 AB - For Gauss-Turan quadrature formulae with an even weight function on the interval [—1, 1] and functions analytic in regions of the complex plane which contain in their interiors a circle of radius greater than 1, the error term is investigated. In some particular cases we prove that the error decreases monotonically to zero. Also, for certain more general cases, we illustrate how to check numerically if this property holds. Some l^2-error estimates are considered. PB - Cambridge University Press T2 - ANZIAM Journal T1 - Monotonicity of the error term in Gauss-Turan quadratures for analytic functions EP - 581 SP - 567 VL - 48 DO - 10.1017/S1446181100003229 ER -
@article{ author = "Milovanović, Gradimir and Spalević, Miodrag", year = "2007", abstract = "For Gauss-Turan quadrature formulae with an even weight function on the interval [—1, 1] and functions analytic in regions of the complex plane which contain in their interiors a circle of radius greater than 1, the error term is investigated. In some particular cases we prove that the error decreases monotonically to zero. Also, for certain more general cases, we illustrate how to check numerically if this property holds. Some l^2-error estimates are considered.", publisher = "Cambridge University Press", journal = "ANZIAM Journal", title = "Monotonicity of the error term in Gauss-Turan quadratures for analytic functions", pages = "581-567", volume = "48", doi = "10.1017/S1446181100003229" }
Milovanović, G.,& Spalević, M.. (2007). Monotonicity of the error term in Gauss-Turan quadratures for analytic functions. in ANZIAM Journal Cambridge University Press., 48, 567-581. https://doi.org/10.1017/S1446181100003229
Milovanović G, Spalević M. Monotonicity of the error term in Gauss-Turan quadratures for analytic functions. in ANZIAM Journal. 2007;48:567-581. doi:10.1017/S1446181100003229 .
Milovanović, Gradimir, Spalević, Miodrag, "Monotonicity of the error term in Gauss-Turan quadratures for analytic functions" in ANZIAM Journal, 48 (2007):567-581, https://doi.org/10.1017/S1446181100003229 . .