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.

引用

页码：802 / 807

页数：6

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