Estimating the error of gauss-turan quadrature formulas using their extensions
Abstract
We consider extensions of Kronrod-type and extensions obtained by generalized averaged Gaussian quadrature formulas for Gauss-Turan quadrature formulas. Existence and uniqueness of these extensions are considered. Their numerical construction is proposed. It is the first general method and is based on a combination of well-known numerical methods for Gauss-Turan, Gauss, Gauss-Kronrod, Anti-Gauss, and generalized averaged Gaussian quadratures. We employ these extensions for estimating the remainder terms in the Gauss-Turan quadratures. Numerical results are presented.
Keywords:
quadrature rule / error estimateSource:
Electronic Transactions on Numerical Analysis, 2014, 41, 1-12Publisher:
- Kent State University
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)
Collections
Institution/Community
Mašinski fakultetTY - JOUR AU - Cvetković, Aleksandar AU - Spalević, Miodrag PY - 2014 UR - https://machinery.mas.bg.ac.rs/handle/123456789/1965 AB - We consider extensions of Kronrod-type and extensions obtained by generalized averaged Gaussian quadrature formulas for Gauss-Turan quadrature formulas. Existence and uniqueness of these extensions are considered. Their numerical construction is proposed. It is the first general method and is based on a combination of well-known numerical methods for Gauss-Turan, Gauss, Gauss-Kronrod, Anti-Gauss, and generalized averaged Gaussian quadratures. We employ these extensions for estimating the remainder terms in the Gauss-Turan quadratures. Numerical results are presented. PB - Kent State University T2 - Electronic Transactions on Numerical Analysis T1 - Estimating the error of gauss-turan quadrature formulas using their extensions EP - 12 SP - 1 VL - 41 UR - https://hdl.handle.net/21.15107/rcub_machinery_1965 ER -
@article{ author = "Cvetković, Aleksandar and Spalević, Miodrag", year = "2014", abstract = "We consider extensions of Kronrod-type and extensions obtained by generalized averaged Gaussian quadrature formulas for Gauss-Turan quadrature formulas. Existence and uniqueness of these extensions are considered. Their numerical construction is proposed. It is the first general method and is based on a combination of well-known numerical methods for Gauss-Turan, Gauss, Gauss-Kronrod, Anti-Gauss, and generalized averaged Gaussian quadratures. We employ these extensions for estimating the remainder terms in the Gauss-Turan quadratures. Numerical results are presented.", publisher = "Kent State University", journal = "Electronic Transactions on Numerical Analysis", title = "Estimating the error of gauss-turan quadrature formulas using their extensions", pages = "12-1", volume = "41", url = "https://hdl.handle.net/21.15107/rcub_machinery_1965" }
Cvetković, A.,& Spalević, M.. (2014). Estimating the error of gauss-turan quadrature formulas using their extensions. in Electronic Transactions on Numerical Analysis Kent State University., 41, 1-12. https://hdl.handle.net/21.15107/rcub_machinery_1965
Cvetković A, Spalević M. Estimating the error of gauss-turan quadrature formulas using their extensions. in Electronic Transactions on Numerical Analysis. 2014;41:1-12. https://hdl.handle.net/21.15107/rcub_machinery_1965 .
Cvetković, Aleksandar, Spalević, Miodrag, "Estimating the error of gauss-turan quadrature formulas using their extensions" in Electronic Transactions on Numerical Analysis, 41 (2014):1-12, https://hdl.handle.net/21.15107/rcub_machinery_1965 .