A construction of higher-rank lattice rules

Timothy N. Langtry

Mathematics and Computers in Simulation (MATCOM), 2001, vol. 55, issue 1, 103-111

Abstract: Lattice rules are quasi-Monte Carlo methods for numerical multiple integration that are based on the selection of an s-dimensional integration lattice. The abscissa set is the intersection of the integration lattice with the unit hypercube. It is well-known that the abscissa set of a lattice rule can be generated by a number of fixed rational vectors. In general, different sets of generators produce different integration lattices and rules, and a given rule has many different generator sets. The rank of the rule is the minimum number of generators required to span the abscissa set.

Keywords: Diophantine approximation; Lattice rules; Cubature (search for similar items in EconPapers)
Date: 2001
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:55:y:2001:i:1:p:103-111

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