On the numerical solution of a nonlinear matrix equation in Markov chains

We consider iterative methods for the minimal nonnegative solution of the matrix equation G = Σ i =0 A i G , where the matrice A , are nonnegative and Σ i =0 A 1 is stochastic. Convergence theory for an inversion free algorithm is established. The convergence rate of this algorithm is shown to be comparable with that of the fastest iteration among three fixed point iterations.