On the growth problem for D-optimal designs
When Gaussian elimination with complete pivoting (GECP) is applied to a real n×n matrix A, we will call g(n, A) the associated growth of the matrix. The problem of determining the largest growth g(n) for various values of n is called the growth problem. It seems quite difficult to establish a. value or close bounds for g(n). For specific values of n (n=1, 2, 3, 4) and for a special category of matrices, such as Hadamard matrices, g(n) has been evaluated exactly. In the present paper, we discuss the maximum determinant and the growth problem of n×n matrices with elements ±1, which are called D-optimal designs. Specific examples of n×n weighing matrices W attaining g(n, W)=n −1 are exhibited.
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