Good Lattice Rules with a Composite Number of Points Based on the Product Weighted Star Discrepancy

Vasile Sinescu () and Stephen Joe ()
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Vasile Sinescu: University of Waikato, Department of Mathematics
Stephen Joe: University of Waikato, Department of Mathematics

A chapter in Monte Carlo and Quasi-Monte Carlo Methods 2006, 2008, pp 645-658 from Springer

Abstract: Summary Rank-1 lattice rules based on a weighted star discrepancy with weights of a product form have been previously constructed under the assumption that the number of points is prime. Here, we extend these results to the non-prime case. We show that if the weights are summable, there exist lattice rules whose weighted star discrepancy is O(n −1+δ ), for any δ > 0, with the implied constant independent of the dimension and the number of lattice points, but dependent on δ and the weights. Then we show that the generating vector of such a rule can be constructed using a component-by-component (CBC) technique. The cost of the CBC construction is analysed in the final part of the paper.

Keywords: Rank-1 lattice rules; weighted star discrepancy; component-by-component construction (search for similar items in EconPapers)
Date: 2008
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-540-74496-2_39

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DOI: 10.1007/978-3-540-74496-2_39

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