Weighted Integral Inequalities in Two Dimensions

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


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
URI https://vuir.vu.edu.au/id/eprint/17642
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 integral inequalities, cubature, singular integration, grid generation
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