Trapezoidal Type Rules from an Inequalities Point of View

Cerone, Pietro and Dragomir, Sever S (1999) Trapezoidal Type Rules from an Inequalities Point of View. RGMIA research report collection, 2 (6).


The article investigates trapezoid type rules and obtains explicit bounds through the use of a Peano kernel approach and the modern theory of inequalities. 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.

Item type Article
Subjects Historical > FOR Classification > 0102 Applied Mathematics
Historical > FOR Classification > 0103 Numerical and Computational Mathematics
Current > Collections > Research Group in Mathematical Inequalities and Applications (RGMIA)
Keywords trapezoidal type rules, analytic inequalities, a priori bounds
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