NEWTON ITERATION FOR NONLINEAR EQUATIONS IN MARKOV-CHAINS

A large number of queueing systems may be modelled as infinite Markov chains for which the transition matrix has a repetitive structure. In order to determine the stationary distribution for these Markov chains , it is necessary to find a particular solution of a non-linear matrix equation. Various iterative algorithms have been proposed to determin e the matrix of interest. We consider here one particular algorithm an d transform it by Newton's method. We show that Newton's algorithm is well defined and converges quadratically in the domain of interest.