In this work we will
consider asynchronous iteration algorithms. As is well known in multiprocessor
computers the parallel application of iterative methods often shows poor
scaling and less optimal parallel efficiency. The ordinary iterative
asynchronous method often has much better parallel efficiency as they almost
never need to wait to communicate between possessors. We will study
probabilistic approach in asynchronous iteration algorithms and present a mathematical description
of this computational process to the multiprocessor environment. The result of
our simple numerical experiments shows a convergence and efficiency of
asynchronous iterative processes for considered nonlinear problems.
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