New convergence results on functional iteration techniques for the numerical solution of M/G/1 type Markov chains

Summary. By performing an accurate analysis of the convergence, we give a complete theoretical explanation of the experimental behaviour of functional iteration techniques for the computation of the minimal nonnegative solution of the matrix equation , arising in the numerical solution of M/G/1 type Markov chains (here the 's are nonnegative matrices such that the matrix is column stochastic). Moreover, we introduce a general class of functional iteration methods, which includes the standard methods, and we give an optimality convergence result in this class. Received September 1, 1995 / Revised version received September 9, 1996