A note on an error bound of Gauss-Turán quadrature with the Chebyshev weight
Abstract
In two BIT papers error expansions in the Gauss and Gauss-Turan quadrature formulas with the Chebyshev weight function of the first kind, in the case when integrand is an analytic function in some region of the complex plane containing the interval of integration in its interior, have been obtained. On the basis of that, using a representation of the remainder term in the form of contour integral over confocal ellipses, the upper bound of the modulus of the remainder term, in the cases when certain parameter s (s є N0) takes the specific values s = 0,1,2, has been obtained. Its form for a general s (s є N0) has been supposed in one of the mentioned papers. Here, we prove that formula.
Keywords:
remainder term / kernel / Gauss-Turan quadrature / error expansion / error bound / elliptic contour / analytic functionSource:
Filomat, 2013, 27, 6, 1037-1042Publisher:
- Univerzitet u Nišu - Prirodno-matematički fakultet - Departmant za matematiku i informatiku, Niš
Funding / projects:
- Approximation of integral and differential operators and applications (RS-MESTD-Basic Research (BR or ON)-174015)
- Methods of Numerical and Nonlinear Analysis with Applications (RS-MESTD-Basic Research (BR or ON)-174002)
DOI: 10.2298/FIL1306037M
ISSN: 0354-5180
WoS: 000322039100009
Scopus: 2-s2.0-84880379598
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Institution/Community
Mašinski fakultetTY - JOUR AU - Milovanović, Gradimir V. AU - Pejčev, Aleksandar AU - Spalević, Miodrag PY - 2013 UR - https://machinery.mas.bg.ac.rs/handle/123456789/1662 AB - In two BIT papers error expansions in the Gauss and Gauss-Turan quadrature formulas with the Chebyshev weight function of the first kind, in the case when integrand is an analytic function in some region of the complex plane containing the interval of integration in its interior, have been obtained. On the basis of that, using a representation of the remainder term in the form of contour integral over confocal ellipses, the upper bound of the modulus of the remainder term, in the cases when certain parameter s (s є N0) takes the specific values s = 0,1,2, has been obtained. Its form for a general s (s є N0) has been supposed in one of the mentioned papers. Here, we prove that formula. PB - Univerzitet u Nišu - Prirodno-matematički fakultet - Departmant za matematiku i informatiku, Niš T2 - Filomat T1 - A note on an error bound of Gauss-Turán quadrature with the Chebyshev weight EP - 1042 IS - 6 SP - 1037 VL - 27 DO - 10.2298/FIL1306037M ER -
@article{ author = "Milovanović, Gradimir V. and Pejčev, Aleksandar and Spalević, Miodrag", year = "2013", abstract = "In two BIT papers error expansions in the Gauss and Gauss-Turan quadrature formulas with the Chebyshev weight function of the first kind, in the case when integrand is an analytic function in some region of the complex plane containing the interval of integration in its interior, have been obtained. On the basis of that, using a representation of the remainder term in the form of contour integral over confocal ellipses, the upper bound of the modulus of the remainder term, in the cases when certain parameter s (s є N0) takes the specific values s = 0,1,2, has been obtained. Its form for a general s (s є N0) has been supposed in one of the mentioned papers. Here, we prove that formula.", publisher = "Univerzitet u Nišu - Prirodno-matematički fakultet - Departmant za matematiku i informatiku, Niš", journal = "Filomat", title = "A note on an error bound of Gauss-Turán quadrature with the Chebyshev weight", pages = "1042-1037", number = "6", volume = "27", doi = "10.2298/FIL1306037M" }
Milovanović, G. V., Pejčev, A.,& Spalević, M.. (2013). A note on an error bound of Gauss-Turán quadrature with the Chebyshev weight. in Filomat Univerzitet u Nišu - Prirodno-matematički fakultet - Departmant za matematiku i informatiku, Niš., 27(6), 1037-1042. https://doi.org/10.2298/FIL1306037M
Milovanović GV, Pejčev A, Spalević M. A note on an error bound of Gauss-Turán quadrature with the Chebyshev weight. in Filomat. 2013;27(6):1037-1042. doi:10.2298/FIL1306037M .
Milovanović, Gradimir V., Pejčev, Aleksandar, Spalević, Miodrag, "A note on an error bound of Gauss-Turán quadrature with the Chebyshev weight" in Filomat, 27, no. 6 (2013):1037-1042, https://doi.org/10.2298/FIL1306037M . .