Finding the stationary states of Markov chains by iterative methods

Yurii Nesterov () and Arkadi Nemirovski ()
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Yurii Nesterov: Université catholique de Louvain, CORE, Belgium
Arkadi Nemirovski: Georgia Institute of Technology, Atlanta, USA

No 2012058, LIDAM Discussion Papers CORE from Université catholique de Louvain, Center for Operations Research and Econometrics (CORE)

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.

Keywords: google problem; page rank; power method; stochastic matrices; global rate of convergence; gradient methods; strong convexity; general norms (search for similar items in EconPapers)
Date: 2012-12-31
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Persistent link: https://EconPapers.repec.org/RePEc:cor:louvco:2012058

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