Finding the Stationary States of Markov Chains by Iterative Methods

Nesterov, Yurii;Nemirovski, Arkadi
(2012)

Files

coredp2012_58web.pdf
  • Open Access
  • Adobe PDF
  • 314.58 KB
Download

Details

Authors
  • Nesterov, YuriiUCLouvain
    Author
  • Nemirovski, ArkadiGeorgia Institute of Technology, Atlanta, USA
    Author
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.
Affiliations

Citations

  • APA
  • Chicago
  • FWB

Nesterov, Y., & Nemirovski, A. (2012). Finding the Stationary States of Markov Chains by Iterative Methods (CORE Discussion Paper 2012/58). https://hdl.handle.net/2078.5/252398