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Mathematical Problems in Engineering
Volume 2015, Article ID 816935, 15 pages
http://dx.doi.org/10.1155/2015/816935
Research Article

A Cost-Effective Smoothed Multigrid with Modified Neighborhood-Based Aggregation for Markov Chains

1School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu 611731, China
2Institute of Mathematics and Computational Science, University of Groningen, 9747 AG Groningen, Netherlands

Received 11 April 2015; Accepted 16 August 2015

Academic Editor: Francesco Braghin

Copyright © 2015 Zhao-Li Shen et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Smoothed aggregation multigrid method is considered for computing stationary distributions of Markov chains. A judgement which determines whether to implement the whole aggregation procedure is proposed. Through this strategy, a large amount of time in the aggregation procedure is saved without affecting the convergence behavior. Besides this, we explain the shortage and irrationality of the Neighborhood-Based aggregation which is commonly used in multigrid methods. Then a modified version is presented to remedy and improve it. Numerical experiments on some typical Markov chain problems are reported to illustrate the performance of these methods.