A probabilistic analysis of asynchronous iteration

We present and analyze a probabilistic model for asynchronous iteration of linear systems. The model is similar in spirit to the chaotic model proposed by Chazan and Miranker in 1969, but with the choice of components and delays being based on probability distributions. We give sufficient conditions and necessary conditions for the expected value of the error to converge to zero. In addition we give sufficient conditions for the variance of the error to converge to zero. These conditions are all weaker than the strong condition of Chazan and Miranker. We also give numerical results of simulations illustrating the theoretical results. (C) 2002 Published by Elsevier Science Inc.