Finding the stationary states of Markov chains by iterative methods

Yurii Nesterov and Arkadi Nemirovski

Applied Mathematics and Computation, 2015, vol. 255, issue C, 58-65

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; Power Method; Stochastic matrices; Global rate of convergence; Gradient methods; Strong convexity (search for similar items in EconPapers)
Date: 2015
References: View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:255:y:2015:i:c:p:58-65

DOI: 10.1016/j.amc.2014.04.053

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