Error estimates for Gaussian quadratures of analytic functions

被引：10
|
作者：
Milovanovic, Gradimir V. [2 ]
Spalevic, Miodrag M. [3 ]
Pranic, Miroslav S. [1 ]
机构：
[1] Univ Banja Luka, Fac Sci, Dept Math & Informat, Banja Luka 51000, Bosnia & Herceg
[2] Univ Nis, Dept Math, Fac Elect Engn, Nish 18000, Serbia
[3] Univ Belgrade, Dept Math, Fac Mech Engn, Belgrade 11000, Serbia
来源：
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS | 2009年 / 233卷 / 03期
关键词：
Gaussian quadrature formula; Chebyshev weight function; Error bound; Remainder term for analytic functions; Contour integral representation;
D O I：
10.1016/j.cam.2009.02.048
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
For analytic functions the remainder term of Gaussian quadrature formula and its Kronrod extension can be represented as a contour integral with a complex kernel. We study these kernels on elliptic contours with foci at the points +/-1 and the sum of semi-axes Q > 1 for the Chebyshev weight functions of the first, second and third kind, and derive representation of their difference. Using this representation and following Kronrod's method of obtaining a practical error estimate in numerical integration, we derive new error estimates for Gaussian quadratures. (C) 2009 Elsevier B.V. All rights reserved.
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页码：802 / 807
页数：6
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