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	2014-03-01T01:17:18Z
dc.date.available	2014-03-01T01:17:18Z
dc.date.issued	2001	en
dc.identifier.issn	0895-4798	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/14446
dc.subject	D-optimal designs	en
dc.subject	symmetric balanced incomplete block designs	en
dc.subject	supplementary difference sets	en
dc.subject	Gaussian elimination	en
dc.subject	growth	en
dc.subject	complete pivoting	en
dc.subject.classification	Mathematics, Applied	en
dc.subject.other	SUPPLEMENTARY DIFFERENCE SETS	en
dc.subject.other	MULTIPLIERS	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.language	English	en
heal.publicationDate	2001	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 - {2s(2) + 2s + 1; s(2), s(2); 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(2s(2) + 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 - {2s(2) + 2s + 1; s(2), s(2); s (s - 1)} sds which yield D-optimal designs can have growth greater than 2 v.	en
heal.publisher	SIAM PUBLICATIONS	en
heal.journalName	SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS	en
dc.identifier.doi	10.1137/S0895479800373644	en
dc.identifier.isi	ISI:000170613100001	en
dc.identifier.volume	23	en
dc.identifier.issue	1	en
dc.identifier.spage	1	en
dc.identifier.epage	14	en