A generalized-network matrix is a matrix that has at most two nonzeros per column. The generalized-network recognition problem for an arbitrary matrix A is the problem of determining a nonsingular matrix T, if one exists, such that T.4 is a generalized-network matrix. This paper presents a polynomial-time algorithm that under an assumption on the combinatorial structure of A solves the generali...

In this paper, a computationally simple approach for damage localization and quantification in beam-like structures is proposed. This method is based on using modal flexibility curvature (MFC) and particle swarm optimization (PSO) algorithm. Analytical studies in the literature have shown that changes in the modal flexibility curvature can be considered as a sensitive and suitable criterion for...

(including the generalized coupled Sylvester matrix equations as special cases) have numerous applications in control and system theory. In this paper, an iterative algorithm is constructed to solve the general coupled matrix equations and their optimal approximation problem over generalized reflexive matrix solution (X1,X2, . . . ,Xq). When the general coupled matrix equations are consistent o...

We develop numerical algorithms for the efficient evaluation of quantities associated with generalized matrix functions [J. B. Hawkins and A. Ben-Israel, Linear and Multilinear Algebra, 1(2), 1973, pp. 163–171]. Our algorithms are based on Gaussian quadrature and Golub–Kahan bidiagonalization. Block variants are also investigated. Numerical experiments are performed to illustrate the effectiven...

A generalized q-Pilbert matrix from [2] is further generalized, introducing one additional parameter. Explicit formulæ are derived for the LU-decomposition and their inverses, as well as the Cholesky decomposition. The approach is to use q-analysis and to leave the justification of the necessary identities to the q-version of Zeilberger’s celebrated algorithm. However, the necessary identities ...

In this paper, the matrix variate ^-generalized normal distribution is introduced. Then its properties are studied. In particular, it is proved that this distribution has maximal entropy in a certain class of distributions.