Block triangular and skew symmetric splitting method for steady state vector of linear system of ergodic block circulant Markov chains (Q2224215)

Summary: In this paper, we determine steady state probability vector \(\pi\) of erogodic block circulant Markov chain using block triangular and skew symmetric method. The homogeneous system \(\pi Q = 0\) is transformed to the non homogeneous regularised linear system \(Ax = b\), and proved that the matrix \(A = Q^{T} + \varepsilon I\) is positive definite for \(\varepsilon > 0\). The contraction factor \(\alpha\) minimises the spectral radius of block iteration matrix of block coefficient matrix \(A\). To improve computing efficiency of the TSS iteration, we employ ITSS iteration. From the numerical results it is clear that the error of TSS iteration method converges rapidly when compared to other existing methods.