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arXiv · 1501.07073

A reduced fast component-by-component construction of lattice point sets with small weighted star discrepancy

Ralph Kritzinger·Helene Laimer
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Abstract

The weighted star discrepancy of point sets appears in the weighted Koksma-Hlawka inequality and thus is a measure for the quality of point sets with respect to their performance in quasi-Monte Carlo algorithms. A special choice of point sets are lattice point sets whose generating vector can be obtained one component at a time such that the resulting lattice point set has a small weighted star discrepancy. In this paper we consider a reduced fast component-by-component algorithm which significantly reduces the construction cost for such generating vectors provided that the weights decrease fast enough.

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Ralph Kritzinger, Helene Laimer. 2015-01-28. A reduced fast component-by-component construction of lattice point sets with small weighted star discrepancy. https://arxiv.org/abs/1501.07073

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