Structure theorems for partially asynchronous iterations of a nonnegative matrix with random delays
نویسندگان
چکیده
We consider partially asynchronous parallel iteration of a fixed nonnegative matrix with stationary ergodic interprocessor communication delays. We study the iteration via a random graph describing the interprocessor influences. Our major result is an invariant description of the rates of convergence of arbitrary sequences of individual processor-time values. In the course of proving this result a number of other invariant properties of the convergence of the iteration are described. The convergence rates that appear in our results are Lyapunov exponents of certain random matrix products derived from the original matrix and the statistics of the delays.
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