The nearest correlation matrix problem is to find a correlation matrix which is closest to a given symmetric matrix under the Frobenius norm. The well studied dual approach is to reformulate this problem as an unconstrained continuously differentiable convex optimization problem. Gradient methods and quasi-Newton methods like BFGS have been used directly to obtain globally convergent methods. S...

It is well known that the determinant of a matrix can only be defined for a square matrix. In this paper, we propose a new definition of the determinant of a rectangular matrix and examine its properties. We apply these properties to squared canonical correlation coefficients, and to squared partial canonical correlation coefficients. The proposed definition of the determinant of a rectangular ...

The nearest correlation matrix problem is to find a correlation matrix which is closest to a given symmetric matrix in the Frobenius norm. The well-studied dual approach is to reformulate this problem as an unconstrained continuously differentiable convex optimization problem. Gradient methods and quasi-Newton methods such as BFGS have been used directly to obtain globally convergent methods. S...

We have obtained all the density matrix elements on six lattice sites for the spin-1/2 Heisenberg chain via the algebraic method based on the quantum Knizhnik-Zamolodchikov equations. Several interesting correlation functions, such as chiral correlation functions, dimer-dimer correlation functions, etc... have been analytically evaluated. Furthermore we have calculated all the eigenvalues of th...

A procedure for extending the size of a Latin hypercube sample (LHS) with rank correlated variables is described and illustrated. The extension procedure starts with an LHS of size m and associated rank correlation matrix C and constructs a new LHS of size 2m that contains the elements of the original LHS and has a rank correlation matrix that is close to the original rank correlation matrix C....

Abstract. Reverse-time migration (RTM) of teleseismic converted and free-surface reflected phases has been successful in helping to constrain the structure of the crust and upper mantle, but its accuracy is to a large extent determined by the background velocity model used in the underlying wave propagation. To this end, we develop a technique for RTM based wave-equation reflection tomography i...

Using the finite Zak transform (FZT) periodic polyphase sequences satisfying the ideal cyclic autocorrelation property and sequence pairs satisfying the optimum cyclic cross correlation property are constructed. The Zak space correlation formula plays a major role in the design of signals having special correlation properties. Sequences defined by permutation matrices in Zak space always satisf...