The matrix functions appear in several applications in engineering and sciences. The computation of these functions almost involved complicated theory. Thus, improving the concept theoretically seems unavoidable to obtain some new relations and algorithms for evaluating these functions. The aim of this paper is proposing some new reciprocal for the function of block anti diagonal matrices. More...

We consider a general QBD process as defining a FIFO queue and obtain the stationary distribution of the sojourn time of a customer in that queue as a matrix exponential distribution, which is identical to a phase-type distribution under a certain condition. Since QBD processes include many queueing models where the arrival and service process are dependent, these results form a substantial gen...

Abstract. A well-known problem in computing some matrix functions iteratively is a lack of a clear, commonly accepted residual notion. An important matrix function for which this is the case is the matrix exponential. Assume, the matrix exponential of a given matrix times a given vector has to be computed. We interpret the sought after vector as a value of a vector function satisfying the linea...

Abstract. A well-known problem in computing some matrix functions iteratively is the lack of a clear, commonly accepted residual notion. An important matrix function for which this is the case is the matrix exponential. Suppose the matrix exponential of a given matrix times a given vector has to be computed. We develop the approach of Druskin, Greenbaum and Knizhnerman (1998) and interpret the ...

We introduce the beta generalized exponential distribution that includes the beta exponential and generalized exponential distributions as special cases. We provide a comprehensive mathematical treatment of this distribution. We derive the moment generating function and the rth moment thus generalizing some results in the literature. Expressions for the density, moment generating function and r...

Exponential estimates and sufficient conditions for the exponential synchronization of complex dynamical networks with bounded time-varying delays are given in terms of linear matrix inequalities (LMIs). A generalized complex networks model involving both neutral delays and retarded ones is presented. The exponential synchronization problem of the complex networks is converted equivalently into...

We propose splitting methods for the computation of the exponential of perturbed matrices which can be written as the sum A = D+εB of a sparse and efficiently exponentiable matrix D with sparse exponential eD and a dense matrix εB which is of small norm in comparison with D. The predominant algorithm is based on scaling the large matrix A by a small number 2−s, which is then exponentiated by ef...

In this paper, the existence, uniqueness and globally exponential stability of the equilibrium point of a dynamic neural network with distributed delays were studied without assumption of boundedness and differentiability of activation functions. Sufficient criteria for existence, uniqueness and global exponential stability of the equilibrium point of such neural networks were obtained based on...