Error bounds and estimates for gauss-turan quadrature formulae of analytic functions
Само за регистроване кориснике
2014
Чланак у часопису (Објављена верзија)
Метаподаци
Приказ свих података о документуАпстракт
We study the error of Gauss-Turan quadrature formulae when functions which are analytic on a neighborhood of the set of integration are considered. A computable upper bound of the error is presented which is valid for arbitrary weight functions. A comparison is made with the exact error, and a number of numerical examples for arbitrary weight functions are given which show the advantages of using such rules as well as the sharpness of the error bound. Also, a comparison is made with the other effective error bounds for some special weight functions appearing in the literature. Asymptotic error estimates when the number of nodes in the quadrature increases are presented. A couple of numerical examples which show their efficiency are included.
Кључне речи:
Gauss-Turan quadrature / error estimate / error bound / ellipse / analytic functionИзвор:
Siam Journal on Numerical Analysis, 2014, 52, 1, 443-467Издавач:
- Siam Publications, Philadelphia
Финансирање / пројекти:
- Методе нумеричке и нелинеарне анализе са применама (RS-MESTD-Basic Research (BR or ON)-174002)
DOI: 10.1137/13091097X
ISSN: 0036-1429
WoS: 000333419300024
Scopus: 2-s2.0-84897858626
Колекције
Институција/група
Mašinski fakultetTY - JOUR AU - Spalević, Miodrag PY - 2014 UR - https://machinery.mas.bg.ac.rs/handle/123456789/1862 AB - We study the error of Gauss-Turan quadrature formulae when functions which are analytic on a neighborhood of the set of integration are considered. A computable upper bound of the error is presented which is valid for arbitrary weight functions. A comparison is made with the exact error, and a number of numerical examples for arbitrary weight functions are given which show the advantages of using such rules as well as the sharpness of the error bound. Also, a comparison is made with the other effective error bounds for some special weight functions appearing in the literature. Asymptotic error estimates when the number of nodes in the quadrature increases are presented. A couple of numerical examples which show their efficiency are included. PB - Siam Publications, Philadelphia T2 - Siam Journal on Numerical Analysis T1 - Error bounds and estimates for gauss-turan quadrature formulae of analytic functions EP - 467 IS - 1 SP - 443 VL - 52 DO - 10.1137/13091097X ER -
@article{ author = "Spalević, Miodrag", year = "2014", abstract = "We study the error of Gauss-Turan quadrature formulae when functions which are analytic on a neighborhood of the set of integration are considered. A computable upper bound of the error is presented which is valid for arbitrary weight functions. A comparison is made with the exact error, and a number of numerical examples for arbitrary weight functions are given which show the advantages of using such rules as well as the sharpness of the error bound. Also, a comparison is made with the other effective error bounds for some special weight functions appearing in the literature. Asymptotic error estimates when the number of nodes in the quadrature increases are presented. A couple of numerical examples which show their efficiency are included.", publisher = "Siam Publications, Philadelphia", journal = "Siam Journal on Numerical Analysis", title = "Error bounds and estimates for gauss-turan quadrature formulae of analytic functions", pages = "467-443", number = "1", volume = "52", doi = "10.1137/13091097X" }
Spalević, M.. (2014). Error bounds and estimates for gauss-turan quadrature formulae of analytic functions. in Siam Journal on Numerical Analysis Siam Publications, Philadelphia., 52(1), 443-467. https://doi.org/10.1137/13091097X
Spalević M. Error bounds and estimates for gauss-turan quadrature formulae of analytic functions. in Siam Journal on Numerical Analysis. 2014;52(1):443-467. doi:10.1137/13091097X .
Spalević, Miodrag, "Error bounds and estimates for gauss-turan quadrature formulae of analytic functions" in Siam Journal on Numerical Analysis, 52, no. 1 (2014):443-467, https://doi.org/10.1137/13091097X . .