New skew Hadamard matrices and their application in edge designs

Georgiou, S; Koukouvinos, C; Stylianou, S

dc.contributor.author	Georgiou, S	en
dc.contributor.author	Koukouvinos, C	en
dc.contributor.author	Stylianou, S	en
dc.date.accessioned	2014-03-01T01:21:07Z
dc.date.available	2014-03-01T01:21:07Z
dc.date.issued	2004	en
dc.identifier.issn	0315-3681	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/16075
dc.relation.uri	http://www.scopus.com/inward/record.url?eid=2-s2.0-13244262763&partnerID=40&md5=e234879f7a56da60d19c427e182b0da9	en
dc.subject	Algorithm	en
dc.subject	Construction	en
dc.subject	Edge design	en
dc.subject	Linear model	en
dc.subject	Skew Hadamard matrix	en
dc.subject.classification	Mathematics, Applied	en
dc.subject.classification	Statistics & Probability	en
dc.title	New skew Hadamard matrices and their application in edge designs	en
heal.type	journalArticle	en
heal.language	English	en
heal.publicationDate	2004	en
heal.abstract	When a large number of variables (factors) are examined in experimental situation it is often anticipated that only few of these will be important. Usually it is not known which of the variables will be the important ones, so it is not known which columns of the experimental design will be of further interest. Many designs have been proposed to be used for screening experiments and to identify the relevant variables. Recently Elster and Neumaier (1995) introduced a new class of experimental designs called edge designs. These designs allow a model-independent estimate of the set of relevant variables, thus providing more robustness than traditional designs. Among others they proposed a construction for edge designs with n - 1 edges, n equivalent to 0 (mod 4) from skew Hadamard matrices of order n. In this paper we use an algorithm to find four (1, - 1) matrices A, B, C, D of order 11, satisfying the relation AA(T) + BBT + CCT + DDT = 44I(11), where A is of skew type. We then use them in the Goethals-Seidel array to obtain new skew Hadamard matrices of order 44. These matrices can be used for the construction of new edge designs with 43 variables and 43 edges. An illustrative simulated example using an edge design in 86 runs is also presented. Key words and phrases: Skew Hadamard matrix, edge design. linear model, algorithm, construction.	en
heal.publisher	UTIL MATH PUBL INC	en
heal.journalName	Utilitas Mathematica	en
dc.identifier.isi	ISI:000226127700008	en
dc.identifier.volume	66	en
dc.identifier.spage	121	en
dc.identifier.epage	136	en