Growth in Gaussian elimination for weighing matrices, W (n, n-1)

Koukouvinos, C; Mitrouli, M; Seberry, J

dc.contributor.author	Koukouvinos, C	en
dc.contributor.author	Mitrouli, M	en
dc.contributor.author	Seberry, J	en
dc.date.accessioned	2014-03-01T01:15:38Z
dc.date.available	2014-03-01T01:15:38Z
dc.date.issued	2000	en
dc.identifier.issn	0024-3795	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/13635
dc.subject	Gaussian elimination	en
dc.subject	growth	en
dc.subject	complete pivoting	en
dc.subject	weighing matrices	en
dc.subject.classification	Mathematics, Applied	en
dc.title	Growth in Gaussian elimination for weighing matrices, W (n, n-1)	en
heal.type	journalArticle	en
heal.identifier.primary	10.1016/S0024-3795(99)00254-2	en
heal.identifier.secondary	http://dx.doi.org/10.1016/S0024-3795(99)00254-2	en
heal.language	English	en
heal.publicationDate	2000	en
heal.abstract	We consider the values for large miners of a skew-Hadamard matrix or conference matrix W of order n and find that maximum n x n minor equals to (n - 1)(n/2), maximum (n - 1) x (n - 1) minor equals to (n - 1)((n/2)-1), maximum (n - 2) x (n - 2) minor equals to 2(n - 1)((n/2)-2) and maximum (n - 3) x (n - 3) minor equals to 4(n - 1)((n/2)-3). This leads us to conjecture that the growth factor for Gaussian elimination (GE) of completely pivoted (CP) skew-Hadamard or conference matrices and indeed any CP weighing matrix of order n and weight n - 1 is n - 1 and that the first and last few pivots are (1, 2, 2, 3 or 4,..., n - 1 or (n - 1)/2, (n - 1)/2, n - 1) for n > 14, We show the unique W(6, 5) has a single pivot pattern and the unique W(8, 7) has at least two pivot structures. We give two pivot patterns for the unique W(10, 9), (C) 2000 Elsevier Science Inc. All rights reserved.	en
heal.publisher	ELSEVIER SCIENCE INC	en
heal.journalName	LINEAR ALGEBRA AND ITS APPLICATIONS	en
dc.identifier.doi	10.1016/S0024-3795(99)00254-2	en
dc.identifier.isi	ISI:000085281600015	en
dc.identifier.volume	306	en
dc.identifier.issue	1-3	en
dc.identifier.spage	189	en
dc.identifier.epage	202	en