✦ LIBER ✦

Notes on lattice rules

✍ Scribed by J.N. Lyness

Publisher: Elsevier Science
Year: 2003
Tongue: English
Weight: 159 KB
Volume: 19
Category: Article
ISSN: 0885-064X
DOI: 10.1016/s0885-064x(03)00005-0

No coin nor oath required. For personal study only.

✦ Synopsis

An elementary introduction to lattices, integration lattices and lattice rules is followed by a description of the role of the dual lattice in assessing the trigonometric degree of a lattice rule. The connection with the classical lattice-packing problem is established: any s-dimensional cubature rule can be associated with an index r ¼ d s =s!N; where d is the enhanced degree of the rule and N its abscissa count. For lattice rules, this is the packing factor of the associated dual lattice with respect to the unit s-dimensional octahedron.

An individual cubature rule may be represented as a point on a plot of r against d: Two of these plots are presented. They convey a clear idea of the relative cost-effectiveness of various individual rules and sequences of rules.

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