Lyness, J. N. & Joe, S.(2006). Determination of the rank of an integration lattice. BIT Numerical Mathematics, 48(1), 79-93.
Permanent Research Commons link: http://hdl.handle.net/10289/2001
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(Λ) directly from the elements of a generator matrix B (possibly in upper triangular lattice form) of the corresponding dual lattice Λ⊥. 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.
This is an author’s version of an article published in the journal: BIT Numerical Mathematics. © 2006 Springer. The original publication is available at www.springerlink.com.