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Weighted Integral Inequalities in Two Dimensions

Hanna, George T and Roumeliotis, John (2001) Weighted Integral Inequalities in Two Dimensions. RGMIA research report collection, 4 (3).

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Abstract

Weighted (or product) double integral inequalities are developed and extended to produce weighted cubature rules. The error bounds are of first and second order and rely on the first few moments of the weight. Various properties of the weight and weight null-spaces are considered. Minimization of the bound produces coupled non-linear equations whose solution furnish optimal weighted cubature grids. These grids are evaluated for some of the more popular weight functions.

Item Type: Article
Uncontrolled Keywords: integral inequalities, cubature, singular integration, grid generation
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: 30 Aug 2012 04:18
Last Modified: 23 May 2013 16:51
URI: http://vuir.vu.edu.au/id/eprint/17642
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