Determination of the rank of an integration lattice

Joe, Stephen; Lyness, J.N.

Determination of the rank of an integration lattice

dc.contributor.author	Joe, Stephen
dc.contributor.author	Lyness, J.N.
dc.date.accessioned	2009-02-10T22:34:35Z
dc.date.available	2009-02-10T22:34:35Z
dc.date.issued	2006
dc.description.abstract	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.	en
dc.format.mimetype	application/pdf
dc.identifier.citation	Lyness, J. N. & Joe, S.(2006). Determination of the rank of an integration lattice. BIT Numerical Mathematics, 48(1), 79-93.	en
dc.identifier.doi	10.1007/s10543-008-0161-4	en
dc.identifier.uri	https://hdl.handle.net/10289/2001
dc.language.iso	en
dc.publisher	Springer Netherlands	en
dc.relation.isPartOf	BIT Numerical Mathematics	en_NZ
dc.relation.uri	http://www.springerlink.com/content/252160005n0061j0/	en
dc.rights	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.	en
dc.subject	mathematics	en
dc.subject	lattice rules	en
dc.subject	rank	en
dc.subject	integration lattice	en
dc.title	Determination of the rank of an integration lattice	en
dc.type	Journal Article	en
pubs.begin-page	79	en_NZ
pubs.elements-id	32932
pubs.end-page	93	en_NZ
pubs.issue	1	en_NZ
pubs.volume	48	en_NZ