dc.contributor.author | Joe, Stephen | |
dc.coverage.spatial | Juan les Pins, FRANCE | en_NZ |
dc.date.accessioned | 2009-02-10T21:32:26Z | |
dc.date.available | 2009-02-10T21:32:26Z | |
dc.date.issued | 2006 | |
dc.identifier.citation | Joe, S.(2006). Construction of Good Rank-1 Lattice Rules Based on the Weighted Star Discrepancy. In H. Niederreiter & D. Talay (Eds), Monte Carlo and Quasi-Monte Carlo Methods 2004 (pp. 181-196). Proceedings of the Sixth International Conference on Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing and of the Second International Conference on Monte Carlo and Probabilistic Methods for Partial Differential Equations. Berlin, Germany: Springer. | en |
dc.identifier.uri | https://hdl.handle.net/10289/2000 | |
dc.description.abstract | The ‘goodness’ of a set of quadrature points in [0, 1]d may be measured by the weighted star discrepancy. If the weights for the weighted star discrepancy are summable, then we show that for n prime there exist n-point rank-1 lattice rules whose weighted star discrepancy is O(n−1+δ) for any δ>0, where the implied constant depends on δ and the weights, but is independent of d and n. Further, we show that the generating vector z for such lattice rules may be obtained using a component-by-component construction. The results given here for the weighted star discrepancy are used to derive corresponding results for a weighted Lp discrepancy. | en |
dc.format.mimetype | application/pdf | |
dc.language.iso | en | |
dc.publisher | Springer, Berlin | en |
dc.relation.uri | http://www.springer.com/math/dyn.+systems/book/978-3-540-25541-3 | en |
dc.rights | This is an author’s version of a paper published in Monte Carlo and Quasi-Monte Carlo Methods 2004. ©2006 Springer. | en |
dc.source | Monte Carlo and Quasi-Monte Carlo Methods 2004 | en_NZ |
dc.subject | mathematics | en |
dc.subject | lattice rules | en |
dc.title | Construction of Good Rank-1 Lattice Rules Based on the Weighted Star Discrepancy | en |
dc.type | Conference Contribution | en |
dc.identifier.doi | 10.1007/3-540-31186-6_12 | en_NZ |
dc.relation.isPartOf | Sixth International Conference on Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing | en_NZ |
pubs.begin-page | 181 | en_NZ |
pubs.elements-id | 16201 | |
pubs.end-page | 196 | en_NZ |
pubs.finish-date | 2004-06-10 | en_NZ |
pubs.start-date | 2004-06-07 | en_NZ |