Determination of the rank of an integration lattice.
The continuing and widespread use of lattice rules for high-dimensional numerical quadrature is driving the development of a rich and detailed theory. Part of this theory is devoted to computer searches for rules, appropriate to particular situations. In some applications, one is interested in obtaining the (lattice) rank of a lattice rule Q({Lambda}) directly from the elements of a generator matrix B (possibly in upper triangular lattice form) of the corresponding dual lattice {Lambda}{sup {perpendicular}}. We treat this problem in detail, demonstrating the connections between this (lattice) rank and the conventional matrix rank deficiency of modulo p versions of B.
- Research Organization:
- Argonne National Lab. (ANL), Argonne, IL (United States)
- Sponsoring Organization:
- USDOE Office of Science (SC)
- DOE Contract Number:
- DE-AC02-06CH11357
- OSTI ID:
- 927729
- Report Number(s):
- ANL/MCS/JA-58948; TRN: US200816%%1185
- Journal Information:
- BIT, Vol. 48, Issue 1 ; Mar. 2008
- Country of Publication:
- United States
- Language:
- ENGLISH
Similar Records
Three- and four-dimensional K-optimal lattice rules of moderate trigonometric degree.
Computing rank-revealing QR factorizations of dense matrices.
Some properties of rank-2 lattice rules
Journal Article
·
Mon Oct 01 00:00:00 EDT 2001
· Math. Comput.
·
OSTI ID:927729
Computing rank-revealing QR factorizations of dense matrices.
Journal Article
·
Mon Jun 01 00:00:00 EDT 1998
· ACM Trans. Math. Software
·
OSTI ID:927729
Some properties of rank-2 lattice rules
Journal Article
·
Sun Oct 01 00:00:00 EDT 1989
· Mathematics of Computation; (USA)
·
OSTI ID:927729