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      On the convergence of a class of multilevel methods for large sparse Markov chains

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      Author(s)
      Buchholz, P.
      Dayar, T.
      Date
      2007
      Source Title
      SIAM Journal on Matrix Analysis and Applications
      Print ISSN
      0895-4798
      Publisher
      Society for Industrial and Applied Mathematics
      Volume
      29
      Issue
      3
      Pages
      1025 - 1049
      Language
      English
      Type
      Article
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      Abstract
      This paper investigates the theory behind the steady state analysis of large sparse Markov chains with a recently proposed class of multilevel methods using concepts from algebraic multigrid and iterative aggregation- disaggregation. The motivation is to better understand the convergence characteristics of the class of multilevel methods and to have a clearer formulation that will aid their implementation. In doing this, restriction (or aggregation) and prolongation (or disaggregation) operators of multigrid are used, and the Kronecker-based approach for hierarchical Markovian models is employed, since it suggests a natural and compact definition of grids (or levels). However, the formalism used to describe the class of multilevel methods for large sparse Markov chains has no influence on the theoretical results derived. © 2007 Society for Industrial and Applied Mathematics.
      Keywords
      Aggregation-disaggregation
      Kronecker-based numerical techniques
      Markov chains
      Multigrid
      Multilevel methods
      Permalink
      http://hdl.handle.net/11693/23304
      Published Version (Please cite this version)
      http://dx.doi.org/10.1137/060651161
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