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

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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 http://hdl.handle.net/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
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

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