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

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	2014-03-01T01:19:41Z
dc.date.available	2014-03-01T01:19:41Z
dc.date.issued	2003	en
dc.identifier.issn	0895-4798	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/15659
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 designs	en
dc.subject.classification	Mathematics, Applied	en
dc.subject.other	MATRICES	en
dc.title	Values of minors of an infinite family of D-optimal designs and their application to the growth problem: II	en
heal.type	journalArticle	en
heal.identifier.primary	10.1137/S0895479801386845	en
heal.identifier.secondary	http://dx.doi.org/10.1137/S0895479801386845	en
heal.language	English	en
heal.publicationDate	2003	en
heal.abstract	We obtain explicit formulae for the values of the 2v - j minors, j = 0, 1, 2, of D-optimal designs of order 2v = x(2) + y(2), v odd, where the design is constructed using two circulant or type 1 incidence matrices of 2 - {s(2) + s + 1; s(s-1)/2, s(s+1)/2; s(s-1)/2} supplementary difference sets (SDS). This allows us to obtain information on the growth problem for families of matrices which have moderately large growth. Some of our theoretical formulae suggest that growth greater than 2 v may occur, 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 -{s(2) + s + 1; s(s-1)/2, s(s+1)/2; s(s-1)/2} SDS, which yield D-optimal designs, can have growth greater than 2v.	en
heal.publisher	SIAM PUBLICATIONS	en
heal.journalName	SIAM Journal on Matrix Analysis and Applications	en
dc.identifier.doi	10.1137/S0895479801386845	en
dc.identifier.isi	ISI:000181153600007	en
dc.identifier.volume	24	en
dc.identifier.issue	3	en
dc.identifier.spage	715	en
dc.identifier.epage	727	en