On the convergence rates of asynchronous iterations

This paper presents a unifying convergence result for asynchronous iterations involving pseudo-contractions in the block-maximum norm. Contrary to previous results which only established asymptotic convergence or studied simplified models of asynchronism, our result allows to bound the convergence rates for both partially and totally asynchronous implementations. Several examples are worked out to demonstrate that our theorem recovers and improves on existing results, and that it allows to characterize the solution times for several classes of asynchronous iterations that have not been addressed before.