F. Robert, M. Charnay and F. Musy, “Iteration Chaotiques Serie-Parablele Pour Equations Non-Linearires de Point Fixe,” Applied Mathematics, Vol. 20, No. 1, 1975, pp. 1-38.
has been cited by the following article:
TITLE: Probabilistic Approach to the Asynchronous Iteration
AUTHORS: A. S. Rasulov, M. T. Bakoev, D. R. Akabirhodjaeva
KEYWORDS: Asynchronous iterations; Linear and Nonlinear Equations; Multiprocessor Computers; Iterative Method with Memory; Probabilistic Approach
JOURNAL NAME: Journal of Applied Mathematics and Physics, Vol.2 No.1, January 9, 2014
ABSTRACT: 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.