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      Steady-state analysis of google-like stochastic matrices with block iterative methods

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      Author
      Dayar, T.
      Noyan, G. N.
      Date
      2011
      Source Title
      Electronic Transactions on Numerical Analysis
      Print ISSN
      1068-9613
      Publisher
      Kent State University
      Volume
      38
      Pages
      69 - 97
      Language
      English
      Type
      Article
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      Abstract
      A Google-like matrix is a positive stochastic matrix given by a convex combination of a sparse, nonnegative matrix and a particular rank one matrix. Google itself uses the steady-state vector of a large matrix of this form to help order web pages in a search engine. We investigate the computation of the steady-state vectors of such matrices using block iterative methods. The block partitionings considered include those based on block triangular form and those having triangular diagonal blocks obtained using cutsets. Numerical results show that block Gauss-Seidel with partitionings based on block triangular form is most often the best approach. However, there are cases in which a block partitioning with triangular diagonal blocks is better, and the Gauss-Seidel method is usually competitive. Copyright © 2011, Kent State University.
      Keywords
      Block iterative methods
      Cutsets
      Google
      PageRank
      Partitionings
      Power method
      Stochastic matrices
      Triangular blocks
      Block iterative method
      Cutsets
      Permalink
      http://hdl.handle.net/11693/21654
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