A CLASS OF ITERATION METHODS BASED ON THE MOSER FORMULA FOR NONLINEAREQUATIONS IN MARKOV-CHAINS

Many stochastic models in queueing, inventory, communications, and dam theories, etc., result in the problem of numerically determining the minimal nonnegative solutions for a class of nonlinear matrix equation s. Various iterative methods have been proposed to determine the matri ces of interest. We propose a new, efficient successive-substitution M oser method and a Newton-Moser method which use the Moser formula (whi ch, originally, is just the Schulz method). These new methods avoid th e inverses of the matrices, and thus considerable savings on the compu tational workloads may be achieved. Moreover, they are much more suita ble for implementing on parallel multiprocessor systems. Under certain conditions, we establish monotone convergence of these new methods, a nd prove local linear convergence for the substitution Moser method an d superlinear convergence for the Newton-Moser method. (C) 1997 Elsevi er Science Inc.