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

作者:Shen, Zhao-Li; Huang, Ting-Zhu*; Carpentieri, Bruno; Wen, Chun
来源:Mathematical Problems in Engineering, 2015, 2015: 816935.
DOI:10.1155/2015/816935

摘要

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.