On an optimal quadrature formula in Sobolev space L2(m)(0,1)

被引：9

作者：

Shadimetov, Kh M. ^{[1
]}

Hayotov, A. R. ^{[1
]}

Nuraliev, F. A. ^{[1
]}

机构：

[1] Uzbek Acad Sci, Inst Math & Informat Technol, Tashkent 100125, Uzbekistan

来源：

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS | 2013年 / 243卷

关键词：

Optimal quadrature formulas; The error functional; The extremal function; SL Sobolev space; Optimal coefficients;

D O I：

10.1016/j.cam.2012.11.010

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper studies the problem of construction of optimal quadrature formulas in the sense of Sard in the space L-2((m))(0, 1). In this paper the quadrature sum consists of values of the integrand at nodes and values of the first derivative of the integrand at the end points of the integration interval. The coefficients of optimal quadrature formulas are found and the norm of the optimal error functional is calculated for arbitrary natural number N and for any m >= 2 using the S.L. Sobolev method which is based on a discrete analog of the differential operator d(2m)/dx(2m). In particular, for m = 2, 3 optimality of the classical Euler-Maclaurin quadrature formula is obtained. Starting from m = 4 new optimal quadrature formulas are obtained. (c) 2012 Elsevier B.V. All rights reserved.

引用

页码：91 / 112

页数：22

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