The experimental analysis of GMRES convergence for solution of Markov chains

The authors consider the impact of the structure of the matrix on the convergence behavior for the GMRES projection method for solving large sparse linear equation systems resulting from Markov chains modeling. Studying experimental results we investigate the number of steps and the rate of convergence of GMRES method and the IWZ preconditioning for the GMRES method. The motivation is to better understand the convergence characteristics of Krylov subspace method and the relationship between the Markov model, the nonzero structure of the coefficient matrix associated with this model and the convergence of the preconditioned GMRES method.