A reduced fast component-by-component construction of lattice point sets with small weighted star discrepancy
Number Theory
2015-11-30 v1
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.
Keywords
Cite
@article{arxiv.1501.07073,
title = {A reduced fast component-by-component construction of lattice point sets with small weighted star discrepancy},
author = {Ralph Kritzinger and Helene Laimer},
journal= {arXiv preprint arXiv:1501.07073},
year = {2015}
}