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

We obtain explicit formulae for the values of the 2v-j minors, j=0,1,2 of D-optimal designs of order 2v = x2 + y2, v odd, where the design is constructed using two circulant or type 1 incidence matrices of $2-\{s^2+s+1;\frac{s(s-1)}{2},\frac{s(s+1)}{2};\frac{s(s-1)}{2}\}$ supplementary difference se...

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Bibliographic Details
Published in:SIAM journal on matrix analysis and applications 2003, Vol.24 (3), p.715-727
Main Authors: KOUKOUVINOS, C, MITROULI, M, SEBERRY, Jennifer
Format: Article
Language:English
Subjects:
Algebra
Applied mathematics
Combinatorics
Combinatorics. Ordered structures
Design optimization
Designs and configurations
Equality
Error analysis
Exact sciences and technology
Linear and multilinear algebra, matrix theory
Mathematics
Numerical analysis
Numerical analysis. Scientific computation
Numerical linear algebra
Sciences and techniques of general use
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Summary:We obtain explicit formulae for the values of the 2v-j minors, j=0,1,2 of D-optimal designs of order 2v = x2 + y2, v odd, where the design is constructed using two circulant or type 1 incidence matrices of $2-\{s^2+s+1;\frac{s(s-1)}{2},\frac{s(s+1)}{2};\frac{s(s-1)}{2}\}$ 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 2v 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 $2-\{s^2+s+1;\frac{s(s-1)}{2},\frac{s(s+1)}{2};\frac{s(s-1)}{2}\}$ SDS, which yield D-optimal designs, can have growth greater than 2v.
ISSN:0895-4798
1095-7162
DOI:10.1137/S0895479801386845