An application of Diophantine approximation to the construction of rank-1 lattice quadrature rules

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dc.contributor.author Langtry, Tim en_US
dc.contributor.editor en_US
dc.date.accessioned 2012-10-12T03:32:49Z
dc.date.available 2012-10-12T03:32:49Z
dc.date.issued 1996 en_US
dc.identifier 2011001139 en_US
dc.identifier.citation Langtry Timothy 1996, 'An application of Diophantine approximation to the construction of rank-1 lattice quadrature rules', American Mathematical Society, vol. 65, no. 216, pp. 1635-1662. en_US
dc.identifier.issn 0025-5718 en_US
dc.identifier.other C1UNSUBMIT en_US
dc.identifier.uri http://hdl.handle.net/10453/17950
dc.description.abstract Lattice quadrature rules were introduced by Frolov (1977), Sloan (1985) and Sloan and Kachoyan (1987). They are quasi-Monte Carlo rules for the approximation of integrals over the unit cube in R(s) and are generalizations of 'number-theoretic' rules introduced by Korobov (1959) and Hlawka (1962)-themselves generalizations, in a sense, of rectangle rules for approximating one-dimensional integrals, and trapezoidal rules for periodic integrands. Error bounds for rank-1 rules are known for a variety of classes of integrands. For periodic integrands with unit period in each variable, these bounds are conveniently characterized by the figure of merit rho, which was originally introduced in the context of number-theoretic rules. The problem of finding good rules of order N (that is, having N nodes) then becomes that of finding rules with large values of rho. This paper presents a new approach, based on the theory of simultaneous Diophantine approximation, which uses a generalized continued fraction algorithm to construct rank-1 rules of high order. en_US
dc.language en_US
dc.publisher American Mathematical Society en_US
dc.relation.isbasedon http://dx.doi.org/10.1090/S0025-5718-96-00758-2 en_US
dc.title An application of Diophantine approximation to the construction of rank-1 lattice quadrature rules en_US
dc.parent Mathematics Of Computation en_US
dc.journal.volume 65 en_US
dc.journal.number 216 en_US
dc.publocation Boston en_US
dc.identifier.startpage 1635 en_US
dc.identifier.endpage 1662 en_US
dc.cauo.name SCI.Mathematical Sciences en_US
dc.conference Verified OK en_US
dc.for 010200 en_US
dc.personcode 830105 en_US
dc.percentage 34 en_US
dc.classification.name Applied Mathematics en_US
dc.classification.type FOR-08 en_US
dc.edition en_US
dc.custom en_US
dc.date.activity en_US
dc.location.activity en_US
dc.description.keywords numerical quadrature; numerical cubature; multiple integration; lattice rules; continued fractions; Diophantine approximation; OPTIMAL INTEGRATION LATTICES; MONTE-CARLO METHODS; MULTIDIMENSIONAL INTEGRATION; MULTIPLE INTEGRATION; ERROR-BOUNDS; VARIABLES; POINTS; SEARCH en_US
dc.staffid en_US
dc.staffid 830105 en_US


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