Linear feedback, irreducibility, and M-matrices

Mixed Matrices — Irreducibility and Decomposition — ∗

This paper surveys mathematical properties of (layered-) mixed matrices with emphasis on irreducibility and block-triangular decomposition. A matrix A is a mixed matrix if A = Q + T , where Q is a “constant” matrix and T is a “generic” matrix (or formal incidence matrix) in the sense that the nonzero entries of T are algebraically independent parameters. A layered mixed (or LM-) matrix is a mix...

M/M/1 Feedback Queue Subject to Catastrophe and Repairment

‎In this paper‎, ‎an M/M/1 queue with instantaneous Bernoulli feedback is studied in the event of server failure‎, ‎the catastrophe occurs and after repair‎, ‎it starts to work again‎. ‎The transient response for the probability function of the system size is presented‎. ‎The steady state analysis of system size probabilities and some performance measures of system are provided‎. ‎Then the resu...

A brief introduction to quaternion matrices and linear algebra and on bounded groups of quaternion matrices

The division algebra of real quaternions, as the only noncommutative normed division real algebra up to isomorphism of normed algebras, is of great importance. In this note, first we present a brief introduction to quaternion matrices and quaternion linear algebra. This, among other things, will help us present the counterpart of a theorem of Herman Auerbach in the setting of quaternions. More ...

Two modified Jacobi methods for M-matrices

Preconditioned SSOR Iterative Method For Linear System With M-Matrices

A preconditioned SSOR iterative method with a multi-parameters preconditioner I + S̃α is proposed. Some convergence and comparison results for αi ∈ [0, 1] are given when the coefficient matrix of linear system A is a nonsingular M−matrix. Numerical example shows that our methods are superior to the basic SSOR iterative method.