Approximating the Stieltjes integral via a weighted trapezoidal rule with applications

被引：2
|
作者：
Dragomir, S. S. [1 ,2 ]
Fedotov, I. [3 ]
机构：
[1] Victoria Univ, Sch Sci & Engn, Melbourne, Vic 8001, Australia
[2] Univ Witwatersrand, Sch Computat & Appl Math, ZA-2050 Johannesburg, South Africa
[3] Tshwane Univ Technol, Dept Math & Stat, ZA-001 Pretoria, South Africa
来源：
MATHEMATICAL AND COMPUTER MODELLING | 2013年 / 57卷 / 3-4期
关键词：
Stieltjes integral; Riemann integral; Generalized trapezoid inequality; Selfadjoint operators; Functions of selfadjoint operators; Spectral representation; OSTROWSKI TYPE INEQUALITIES; GRUSS INEQUALITY; MAPPINGS;
D O I：
10.1016/j.mcm.2012.07.023
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 error bounds in approximating the weighted Riemann-Stieltjes integral integral(b)(a)f(t)g(t)d alpha(t) by the weighted trapezoidal rule f(a)+f(b)/2 integral(b)(a)g(t) d alpha(t). Applications for continuous functions of selfadjoint operators in complex Hilbert spaces are given as well. (C) 2012 Elsevier Ltd. All rights reserved.
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页码：602 / 611
页数：10
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