Values of minors of an infinite family of D-optimal designs and their application to the growth problem

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	2014-03-01T01:52:02Z
dc.date.available	2014-03-01T01:52:02Z
dc.date.issued	2002	en
dc.identifier.issn	08954798	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/26536
dc.subject	Complete pivoting	en
dc.subject	D-optimal designs	en
dc.subject	Gaussian elimination	en
dc.subject	Growth	en
dc.subject	Supplementary difference sets	en
dc.subject	Symmetric balanced incomplete block designs	en
dc.title	Values of minors of an infinite family of D-optimal designs and their application to the growth problem	en
heal.type	journalArticle	en
heal.identifier.primary	10.1137/S0895479800373644	en
heal.identifier.secondary	http://dx.doi.org/10.1137/S0895479800373644	en
heal.publicationDate	2002	en
heal.abstract	We obtain explicit formulae for the values of the 2v - j minors, j = 0,1,2, of Doptimal designs of order 2v = x2 + y2, v odd, where the design is constructed using two circulant or type 1 incidence matrices of 2- {2s2 + 2s + 1; s2, s2; s(s - 1) } supplementary difference sets (sds). This allows us to obtain information on the growth problem for families of matrices with moderate growth. Some of our theoretical formulae imply growth greater than 2(2s2 + 2s + 1) but experimentation has not yet supported this result. An open problem remains to establish whether the (1, -1) completely pivoted (CP) incidence matrices of 2 - {2s2 + 2s + 1; s2, s2; s(s - 1)} sds which yield D-optimal designs can have growth greater than 2v.	en
heal.journalName	SIAM Journal on Matrix Analysis and Applications	en
dc.identifier.doi	10.1137/S0895479800373644	en
dc.identifier.volume	23	en
dc.identifier.issue	1	en
dc.identifier.spage	1	en
dc.identifier.epage	14	en