Approximating the Riemann-Stieltjes integral by a trapezoidal quadrature rule with applications

被引：16

作者：

Dragomir, S. S. ^{[1
,2
]}

机构：

[1] Victoria Univ, Sch Sci & Engn, Melbourne, MC 8001, Australia

[2] Univ Witwatersrand, Sch Computat & Appl Math, ZA-2050 Johannesburg, South Africa

来源：

MATHEMATICAL AND COMPUTER MODELLING | 2011年 / 54卷 / 1-2期

关键词：

Riemann-Stieltjes integral; Trapezoidal quadrature rule; Selfadjoint operators; Functions of selfadjoint operators; Spectral representation; Inequalities for selfadjoint operators;

D O I：

10.1016/j.mcm.2011.02.006

中图分类号：

TP39 [计算机的应用];

学科分类号：

081203 ; 0835 ;

摘要：

In this paper we provide sharp bounds for the error in approximating the Riemann-Stieltjes integral integral(b)(a)f(t)du(t) by the trapezoidal rule f(a) + f (b)/2 . [u(b) -u(a)] under various assumptions for the integrand f and the integrator u for which the above integral exists. Applications for continuous functions of selfadjoint operators in Hilbert spaces are provided as well. (C) 2011 Elsevier Ltd. All rights reserved.

引用

页码：243 / 260

页数：18