Convergence Analysis of Triangular and Symmetric Splitting Method for Steady State Vector of Regularized Linear System with Block Circulant Matrices
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Abstract
In this paper, triangular and symmetric splitting method is applied for determining the steady state probability vector of regularized linear system The homogeneous system where is block stochastic rate matrix, is transformed into regularized non-homogeneous linear system by using preconditioned matrix with the small perturbation It is proved that the regularized matrix is positive definite. In this convergence analysis of the (triangular and symmetric) TS iteration method, both relative error and absolute error are considered. From the numerical results, it is concluded that TS iteration method converge rapidly when compared with other existing methods.
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