Error Estimations of Turan Formulas with Gori-Micchelli and Generalized Chebyshev Weight Functions
Abstract
S. Li in [Studia Sci. Math. Hungar. 29 (1994) 71-83] proposed a Kronrod type extension to the well-known Turan formula. He showed that such an extension exists for any weight function. For the classical Chebyshev weight function of the first kind, Li found the Kronrod extension of Turan formula that has all its nodes real and belonging to the interval of integration, [-1, 1]. In this paper we show the existence and the uniqueness of the additional two cases - the Kronrod exstensions of corresponding Gauss-Turan quadrature formulas for special case of Gori-Micchelli weight function and for generalized Chebyshev weight function of the second kind, that have all their nodes real and belonging to the integration interval [-1, 1]. Numerical results for the weight coefficients in these cases are presented, while the analytic formulas of the nodes are known.
Keywords:
Kronrod extension / Gori-Micchelli weight function / Generalized Chebyshev weight function of the second kind / Gauss-Turan quadrature formulas / Error estimationSource:
Filomat, 2018, 32, 20, 6927-6936Publisher:
- Univerzitet u Nišu - Prirodno-matematički fakultet - Departmant za matematiku i informatiku, Niš
Funding / projects:
- Methods of Numerical and Nonlinear Analysis with Applications (RS-MESTD-Basic Research (BR or ON)-174002)
DOI: 10.2298/FIL1820927M
ISSN: 0354-5180
WoS: 000463447500009
Scopus: 2-s2.0-85061348694
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Institution/Community
Mašinski fakultetTY - JOUR AU - Mihić, Ljubica AU - Pejčev, Aleksandar AU - Spalević, Miodrag PY - 2018 UR - https://machinery.mas.bg.ac.rs/handle/123456789/2798 AB - S. Li in [Studia Sci. Math. Hungar. 29 (1994) 71-83] proposed a Kronrod type extension to the well-known Turan formula. He showed that such an extension exists for any weight function. For the classical Chebyshev weight function of the first kind, Li found the Kronrod extension of Turan formula that has all its nodes real and belonging to the interval of integration, [-1, 1]. In this paper we show the existence and the uniqueness of the additional two cases - the Kronrod exstensions of corresponding Gauss-Turan quadrature formulas for special case of Gori-Micchelli weight function and for generalized Chebyshev weight function of the second kind, that have all their nodes real and belonging to the integration interval [-1, 1]. Numerical results for the weight coefficients in these cases are presented, while the analytic formulas of the nodes are known. PB - Univerzitet u Nišu - Prirodno-matematički fakultet - Departmant za matematiku i informatiku, Niš T2 - Filomat T1 - Error Estimations of Turan Formulas with Gori-Micchelli and Generalized Chebyshev Weight Functions EP - 6936 IS - 20 SP - 6927 VL - 32 DO - 10.2298/FIL1820927M ER -
@article{ author = "Mihić, Ljubica and Pejčev, Aleksandar and Spalević, Miodrag", year = "2018", abstract = "S. Li in [Studia Sci. Math. Hungar. 29 (1994) 71-83] proposed a Kronrod type extension to the well-known Turan formula. He showed that such an extension exists for any weight function. For the classical Chebyshev weight function of the first kind, Li found the Kronrod extension of Turan formula that has all its nodes real and belonging to the interval of integration, [-1, 1]. In this paper we show the existence and the uniqueness of the additional two cases - the Kronrod exstensions of corresponding Gauss-Turan quadrature formulas for special case of Gori-Micchelli weight function and for generalized Chebyshev weight function of the second kind, that have all their nodes real and belonging to the integration interval [-1, 1]. Numerical results for the weight coefficients in these cases are presented, while the analytic formulas of the nodes are known.", publisher = "Univerzitet u Nišu - Prirodno-matematički fakultet - Departmant za matematiku i informatiku, Niš", journal = "Filomat", title = "Error Estimations of Turan Formulas with Gori-Micchelli and Generalized Chebyshev Weight Functions", pages = "6936-6927", number = "20", volume = "32", doi = "10.2298/FIL1820927M" }
Mihić, L., Pejčev, A.,& Spalević, M.. (2018). Error Estimations of Turan Formulas with Gori-Micchelli and Generalized Chebyshev Weight Functions. in Filomat Univerzitet u Nišu - Prirodno-matematički fakultet - Departmant za matematiku i informatiku, Niš., 32(20), 6927-6936. https://doi.org/10.2298/FIL1820927M
Mihić L, Pejčev A, Spalević M. Error Estimations of Turan Formulas with Gori-Micchelli and Generalized Chebyshev Weight Functions. in Filomat. 2018;32(20):6927-6936. doi:10.2298/FIL1820927M .
Mihić, Ljubica, Pejčev, Aleksandar, Spalević, Miodrag, "Error Estimations of Turan Formulas with Gori-Micchelli and Generalized Chebyshev Weight Functions" in Filomat, 32, no. 20 (2018):6927-6936, https://doi.org/10.2298/FIL1820927M . .