Notes on lattice rules.
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 {rho}={delta}{sup s}/s!N, where {delta} 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 {rho} against {delta}. Two of these plots are presented. They convey a clear idea of the relative cost-effectiveness of various individual rules and sequences of rules.
- Research Organization:
- Argonne National Laboratory (ANL)
- Sponsoring Organization:
- SC
- DOE Contract Number:
- AC02-06CH11357
- OSTI ID:
- 961207
- Report Number(s):
- ANL/MCS/JA-45434
- Journal Information:
- J. Complexity, Journal Name: J. Complexity Journal Issue: 3 ; 2003 Vol. 19
- Country of Publication:
- United States
- Language:
- ENGLISH
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