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Midpoint Type Rules from an Inequalities Point of View

Cerone, Pietro and Dragomir, Sever S (1999) Midpoint Type Rules from an Inequalities Point of View. RGMIA research report collection, 2 (7).

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The article investigates interior point rules which contain the midpoint as a special case, and obtains explicit bounds through the use of a Peano kernel approach and the modern theory of inequalities. Thus the simplest open Newton-Cotes rules are examined. Both Riemann-Stieltjes and Riemann integrals are evaluated with a variety of assumptions about the integrand enabling the characterisation of the bound in terms of a variety of norms. Perturbed quadrature rules are obtained through the use of Grüss, Chebychev and Lupaş inequalities, producing a variety of tighter bounds. The implementation is demonstrated through the investigation of a variety of composite rules based on inequalities developed. The analysis allows the determination of the partition required that would assure that the accuracy the result would be within a prescribed error tolerance. It is demonstrated that the bounds of the approximations are equivalent to those obtained from a Peano kernel that produces Trapezoidal type rules.

Item Type: Article
Uncontrolled Keywords: interior point type rules, analytic inequalities, a priori 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 00:46
Last Modified: 23 May 2013 16:49
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