Component-by-component construction of good intermediate-rank lattice rules

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dc.contributor.authorKuo, Frances Y.
dc.contributor.authorJoe, Stephen
dc.date.accessioned2009-01-06T20:05:58Z
dc.date.available2009-01-06T20:05:58Z
dc.date.issued2003
dc.description.abstractIt is known that the generating vector of a rank-1 lattice rule can be constructed component-by-component to achieve strong tractability error bounds in both weighted Korobov spaces and weighted Sobolev spaces. Since the weights for these spaces are nonincreasing, the first few variables are in a sense more important than the rest. We thus propose to copy the points of a rank-1 lattice rule a number of times in the first few dimensions to yield an intermediate-rank lattice rule. We show that the generating vector (and in weighted Sobolev spaces, the shift also) of an intermediate-rank lattice rule can also be constructed component-by-component to achieve strong tractability error bounds. In certain circumstances, these bounds are better than the corresponding bounds for rank-1 lattice rules.en
dc.format.mimetypeapplication/pdf
dc.identifier.citationKuo, F.Y. & Joe, S.(2003). Component-by-component construction of good intermediate-rank lattice rules. SIAM Journal of Numerical Analysis, 41(4), 1465-1486.en
dc.identifier.doi10.1137/S0036142902407162en_NZ
dc.identifier.urihttps://hdl.handle.net/10289/1740
dc.language.isoen
dc.publisherSociety for Industrial and Applied Mathematicsen
dc.relation.isPartOfSIAM Journal on Numerical Analysisen_NZ
dc.relation.urihttp://siamdl.aip.org/getpdf/servlet/GetPDFServlet?filetype=pdf&id=SJNAAM000041000004001465000001&idtype=cvipsen
dc.rightsThis is an author’s version of an article published in the journal: SIAM Journal of Numerical Analysis. © 2003 Society for Industrial and Applied Mathematics. Used with permission.en
dc.subjectmathematicsen
dc.subjectquasi-Monte Carlo methodsen
dc.subjectintermediate-rank lattice rulesen
dc.subjectworst-case erroren
dc.subjecttractabilityen
dc.titleComponent-by-component construction of good intermediate-rank lattice rulesen
dc.typeJournal Articleen
pubs.begin-page1465en_NZ
pubs.elements-id29448
pubs.end-page1486en_NZ
pubs.issue4en_NZ
pubs.volume41en_NZ
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