Back
 JAMP  Vol.2 No.1 , January 2014
Probabilistic Approach to the Asynchronous Iteration
A. S. Rasulov*, M. T. Bakoev, D. R. Akabirhodjaeva
Show more
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.
Keywords: Asynchronous iterations; Linear and Nonlinear Equations; Multiprocessor Computers; Iterative Method with Memory; Probabilistic Approach
Cite this paper: Rasulov, A. , Bakoev, M. and Akabirhodjaeva, D. (2014) Probabilistic Approach to the Asynchronous Iteration. Journal of Applied Mathematics and Physics, 2, 32-40. doi: 10.4236/jamp.2014.21006.
References

[1]   A. S. Rasulov, “Asynchronous and Statistical Algorithms for the Solution Linear and Nonlinear Equations,” PhD Dissertation, Novosibirsk, 1992, Russia. http://fizmathim.com/asinhronno-statisticheskie-algoritmy-resheniya-lineynyh-i-nelineynyh-uravneniy

[2]   S. M. Ermakov, V. V. Nekrutkin and A. S. Sipin, “Random Processes for Classical Equations of Mathematical Physics,” Kluwer Academic Publication, London, 1989.

[3]   G. M. Baudet, “Iterative Methods for Asynchronous Multiprocessors, High Speed Computer and Algorithm Organization,” In: D. Kuck, D. Lawrie and A. Sameh, Eds., Academic Press, New York, 1977, pp. 309-310.

[4]   G. M. Baudet, “Asynchronous Iterative Methods for Multiprocessors,” Journal of Associated Computation, Vol. 25. No. 2, 1978, pp. 226-244. http://dx.doi.org/10.1145/322063.322067

[5]   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.

[6]   D. Chazan and W. Miranker, “Chaotic Relaxation,” Linear Algebra and Its Applications, Vol. 2, 1969, pp. 199-229. http://dx.doi.org/10.1016/0024-3795(69)90028-7

[7]   J. D. Donelly, “Periodic Chotic Relaxation,” Linear Algebra and Its Applications, No. 2, 1971, pp. 117-128. http://dx.doi.org/10.1016/0024-3795(71)90033-4

[8]   B. B. Nesterenko and V. A. Marchuk, “Basics of Asynchronous Methods for Parallel Calculations,” Kiev. Nauka-Dumka, 1989, p. 176, Monograph (in Russian).

[9]   W. Shooman, “Orthogonal Processing, Parallel Processors, System, Technologies and Application,” 1970, pp. 297-308.

[10]   V. N. Belectkiy, “Multiprocessors and Parallel Structures with Organization of Asynchronous Calculations,” Kiev, Nauka-Dumka, 1988, p. 240 (in Russian).

 
 
Top