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).
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 |
| 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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