dc.contributor.author Joe, Stephen dc.contributor.author Sinescu, Vasile dc.coverage.spatial Conference held at 'Monte Carlo and Quasi-Monte Carlo Methods 2006' en_NZ dc.date.accessioned 2009-02-11T00:36:02Z dc.date.available 2009-02-11T00:36:02Z dc.date.issued 2008 dc.identifier.citation Sinescu, V. & Joe, S.(2008). Good lattice rules with a composite number of points based on the product weighted star discrepancy. In H. Niederreiter & D. Talay (Eds), Monte Carlo and Quasi-Monte Carlo Methods 2006(pp. 645-658). Berlin, Germany: Springer. en dc.identifier.uri https://hdl.handle.net/10289/2004 dc.description.abstract 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. en dc.format.mimetype application/pdf dc.language.iso en dc.publisher Springer Berlin Heidelberg en dc.relation.uri http://www.springerlink.com/content/lul76nj618433987/ en dc.rights This is an author’s version of article published in the book: Monte Carlo and Quasi-Monte Carlo Methods 2006. en dc.source 7th International Conference on Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing en_NZ dc.subject mathematics en dc.subject rank-1 lattice rules en dc.subject weighted start discrepancy en dc.subject component-by-component construction en dc.title Good lattice rules with a composite number of points based on the product weighted star discrepancy en dc.type Chapter in Book en dc.identifier.doi 10.1007/978-3-540-74496-2_39 en dc.relation.isPartOf Seventh International Conference on Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing, Germany; 14-18 August 2006 en_NZ pubs.begin-page 645 en_NZ pubs.elements-id 17681 pubs.end-page 658 en_NZ pubs.finish-date 2006-08-18 en_NZ pubs.start-date 2006-08-14 en_NZ
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