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

In this paper we provide sharp bounds for the error in approximating the Riemann–Stieltjes integral ∫ a b f ( t ) d u ( 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. Appl...

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Bibliographic Details
Published in:Mathematical and computer modelling 2011-07, Vol.54 (1), p.243-260
Main Author: Dragomir, S.S.
Format: Article
Language:English
Subjects:
Approximations and expansions
Exact sciences and technology
Functions of selfadjoint operators
Inequalities for selfadjoint operators
Mathematical analysis
Mathematics
Methods of scientific computing (including symbolic computation, algebraic computation)
Numerical analysis
Numerical analysis. Scientific computation
Numerical approximation
Real functions
Riemann–Stieltjes integral
Sciences and techniques of general use
Selfadjoint operators
Spectral representation
Trapezoidal quadrature rule
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Summary:In this paper we provide sharp bounds for the error in approximating the Riemann–Stieltjes integral ∫ a b f ( t ) d u ( 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.
ISSN:0895-7177
1872-9479
DOI:10.1016/j.mcm.2011.02.006