Steady state probability vector of positive definite regularized linear systems of circulant stochastic matrices

Abstract

In this paper, we introduce a splitting method, namely triangular and symmetric splitting (TS) method in order to solve the regularized linear system associated with stochastic matrices. We proved that the regularized matrix is positive definite, where I is the real identity matrix of designated dimension, , and Q is the stochastic circulant rate matrix. Analysis shows that the iterative solution of TS method converges unconditionally to the unique solution of the regularized linear system. From the numerical results, it is clear that the solution of proposed method converges rapidly when compared to the existing methods.