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See detailRemoving the saturation assumption in Bank-Weiser error estimator analysis in dimension three
Bulle, Raphaël UL; Chouly, Franz; Hale, Jack UL et al

in Applied Mathematics Letters (2020), 107

We provide a new argument proving the reliability of the Bank-Weiser estimator for Lagrange piecewise linear finite elements in both dimension two and three. The extension to dimension three constitutes ... [more ▼]

We provide a new argument proving the reliability of the Bank-Weiser estimator for Lagrange piecewise linear finite elements in both dimension two and three. The extension to dimension three constitutes the main novelty of our study. In addition, we present a numerical comparison of the Bank-Weiser and residual estimators for a three-dimensional test case. [less ▲]

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See detailSymmetric approximations of pseudo-Boolean functions with applications to influence indexes
Marichal, Jean-Luc UL; Mathonet, Pierre UL

in Applied Mathematics Letters (2012), 25(8), 1121-1126

We introduce an index for measuring the influence of the $k$th smallest variable on a pseudo-Boolean function. This index is defined from a weighted least squares approximation of the function by linear ... [more ▼]

We introduce an index for measuring the influence of the $k$th smallest variable on a pseudo-Boolean function. This index is defined from a weighted least squares approximation of the function by linear combinations of order statistic functions. We give explicit expressions for both the index and the approximation and discuss some properties of the index. Finally, we show that this index subsumes the concept of system signature in engineering reliability and that of cardinality index in decision making. [less ▲]

Detailed reference viewed: 72 (4 UL)