We study the question of finding the maximal determinant of matrices of odd order with entries ±1. The most general upper bound on the maximal determinant, due to Barba, can only be achieved when the order is the sum of two consecutive squares. It is conjectured that the bound is always attained in such cases. Apart from these, only in orders 3, 7, 9, 11, 17 and 21 has the maximal value been es...

We consider a general bitangential interpolation problem for matrix Schur functions and focus mainly on the case when the associated Pick matrix is singular (and positive semidefinite). Descriptions of the set of all solutions are given in terms of special linear fractional transformations which are obtained using two quite different approaches. As applications of the obtained results we consid...

The maximum-entropy sampling problem is a fundamental and challenging combinatorial-optimization problem, with application in spatial statistics. It asks to find maximum-determinant order-s principal submatrix of an order-n covariance matrix. Exact solution methods for this NP-hard are based on branch-and-bound framework. Many the known upper bounds optimal value convex optimization. We present...

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.

The authors recently proposed a simplex-based Tardos’ algorithm which is strongly polynomial if the coefficient matrix is totally unimodular and the auxiliary problems are non-degenerate. Motivated by the algorithmic practically of such methods, we introduce a modification which circumvents the determination of the largest sub-determinant while keeping the same theoretical performance. Assuming...

Parameter estimation method for the spatial autoregression model (SAR) is important because of the many application domains, such as regional economics, ecology, environmental management, public safety, transportation, public health, business, travel and tourism. However, it is computationally very expensive because of the need to compute the determinant of a large matrix due to Maximum Likelih...

BACKGROUND The aims of this study were to investigate the relationships between the maximum isometric toe flexor muscle strength (TFS) and cross-sectional area (CSA) of the plantar intrinsic and extrinsic muscles and to identify the major determinant of maximum TFS among CSA of the plantar intrinsic and extrinsic muscles. METHODS Twenty six young healthy participants (14 men, 12 women; age, 2...

magnetotelluric (mt) method is an electromagnetic method which provides information about subsurface conductivity structures using earth's natural electromagnetic fields. static shift is one of disorders arising from shallow conductors; therefore static shift must be corrected as one of mt data processing steps. in the absence of sufficient information about the near surface distortions, w...