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Finding the stationary states of Markov chains by iterative methods

Author

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  • NESTEROV, Yurii

    (Université catholique de Louvain, CORE, Belgium)

  • NEMIROVSKI, Arkadi

    (Georgia Institute of Technology, Atlanta, USA)

Abstract

In this paper, we develop new methods for approximating dominant eigenvector of column-stochastic matrices. We analyze the Google matrix, and present an averaging scheme with linear rate of convergence in terms of 1-norm distance. For extending this convergence result onto general case, we assume existence of a positive row in the matrix. Our new numerical scheme, the Reduced Power Method (RPM), can be seen as a proper averaging of the power iterates of a reduced stochastic matrix. We analyze also the usual Power Method (PM) and obtain convenient conditions for its linear rate of convergence with respect to 1-norm.

Suggested Citation

  • NESTEROV, Yurii & NEMIROVSKI, Arkadi, 2012. "Finding the stationary states of Markov chains by iterative methods," LIDAM Discussion Papers CORE 2012058, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    • Handle: RePEc:cor:louvco:2012058
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    References listed on IDEAS

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