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Three Point Quadrature Rules Involving, at Most, a First Derivative

Cerone, Pietro and Dragomir, Sever S (1999) Three Point Quadrature Rules Involving, at Most, a First Derivative. RGMIA research report collection, 2 (4).

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Abstract

A unified treatment of three point quadrature rules is presented in which the classical rules of mid-point, trapezoidal and Simpson type are recaptured as particular cases. Riemann integrals are approximated for the derivative of the integrand belonging to a variety of norms. The Grüss inequality and a number of variants are also presented which provide a variety of inequalities that are suitatable for numerical implementation. Mappings that are of bounded total variation, Lipschitzian and monotonic are also investigated with relation to Riemann-Stieltjes integrals. Explicit a priori bounds are provided allowing the determination of the partition required to achieve a prescribed error tolerance. It is demonstrated that with the above classes of functions, the average of a mid-point and trapezoidal type rule produces the best bounds.

Item Type: Article
Uncontrolled Keywords: integral inequalities, three point quadrature formulae, explicit bounds
Subjects: FOR Classification > 0102 Applied Mathematics
FOR Classification > 0103 Numerical and Computational Mathematics
Collections > Research Group in Mathematical Inequalities and Applications (RGMIA)
Depositing User: Research Group in Mathematical Inequalities and Applications
Date Deposited: 19 Jul 2012 01:34
Last Modified: 23 May 2013 16:49
URI: http://vuir.vu.edu.au/id/eprint/17231
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