Some D-optimal chemical balance weighing designs: theory and examples
نویسندگان
چکیده
منابع مشابه
D-optimal weighing designs for four and five objects
For j = 4 and j = 5 and all d j, the maximum value of detXX , where X runs through all j d (0,1)-matrices, is determined along with a matrix X0 for which the maximum determinant is attained. In the theory of statistical designs, X0 is called a D-optimal design matrix. Design matrices that were previously thought to be D-optimal, are shown here to be D-optimal.
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Let Mm,n(0, 1) denote the set of all m× n (0,1)-matrices and let G(m,n) = max{detXX : X ∈Mm,n(0, 1)}. In this paper we exhibit some new formulas for G(m,n) where n ≡ −1 (mod 4). Specifically, for m = nt+r where 0 ≤ r < n, we show that for all sufficiently large t, G(nt+r, n) is a polynomial in t of degree n that depends on the characteristic polynomial of the adjacency matrix of a certain regul...
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ژورنال
عنوان ژورنال: Biometrical Letters
سال: 2017
ISSN: 1896-3811
DOI: 10.1515/bile-2017-0008