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Finding the stationary states of Markov chains by iterative methods

Author

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  • Nesterov, Yurii
  • Nemirovski, Arkadi

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, 2015. "Finding the stationary states of Markov chains by iterative methods," Applied Mathematics and Computation, Elsevier, vol. 255(C), pages 58-65.
    • Handle: RePEc:eee:apmaco:v:255:y:2015:i:c:p:58-65
    DOI: 10.1016/j.amc.2014.04.053
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    Cited by:

    1. Shikhman, V. & Nesterov, Yu. & Ginsburgh, V., 2018. "Power method tâtonnements for Cobb–Douglas economies," Journal of Mathematical Economics, Elsevier, vol. 75(C), pages 84-92.

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