A matrix P ∈ Rn×n is said to be a symmetric orthogonal matrix if P = P T = P−1. A matrix A ∈ Rn×n is said to be generalized centro-symmetric (generalized central anti-symmetric )with respect to P , if A = PAP (A = −PAP ). In this paper, an iterative method is constructed to solve the generalized centrosymmetric solutions of a linear matrix equation AXB + CY D = E, with real pair matrices X and ...

Recently, some authors proposed the use of symmetric weightsfor computing the elements of cross-efficiency matrix. In spite ofthe fact that the proposed method decreases the number of zeroweights, a large number of zero weights may still exist among inputand output symmetric weights. To decrease the number of input andoutput symmetric weights, this paper improves the proposed secondarygoal mode...

In this paper, we show that a matrix A in Mn(C) that has n coneigenvectors, where coneigenvaluesassociated with them are distinct, is condiagonalizable. And also show that if allconeigenvalues of conjugate-normal matrix A be real, then it is symmetric.  

Our study proposes a novel MPI-only parallel programming model with improved performance for SMP clusters. By rescheduling tasks in a typical flat MPI solution, our model forces processors of an SMP node to work in different phases, thereby avoiding unneccessary communication and computation bottlenecks. This study achieves a significant performance improvement with a minimal programming effort...

Matrix variables are ubiquitous in modern optimization, in part because variational properties of useful matrix functions often expedite standard optimization algorithms. Convexity is one important such property: permutation-invariant convex functions of the eigenvalues of a symmetric matrix are convex, leading to the wide applicability of semidefinite programming algorithms. We prove the analo...

In this paper for a given prescribed Ritz values that satisfy in the some special conditions, we find a symmetric nonnegative matrix, such that the given set be its Ritz values.

In this paper, the optical properties of one dimensional fractal structures are investigated. We consider six typical fractal photonic structures: the symmetric dual cantor-like fractal structure, the asymmetric dual cantor-like fractal structure, the single cantor-like fractal structure, the symmetric dual golden-section fractal structure, the asymmetric dual golden-section fractal structure a...