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A new iterative method for solving Large-Scale Markov chains

  • Abderezak Touzene
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 977)

Abstract

In this paper, we propose a new iterative method for solving Large-Scale Markov chains. This method combines some of the well known techniques such as aggregation, Gauss-Seidel effect and overrelaxation. Our aim is to take advantage of those techniques for accelerating the convergence rate.

Keywords

Markov Chain Krylov Subspace GMRES Method Arnoldi Method Aggregate System 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    W-L Cao and W.J. Stewart. Iterative aggregation/disaggregation techniques for nearly uncoupled Markov chains. J. Assoc. Comp. Mach. 32, 3 (1985), 702–719.Google Scholar
  2. 2.
    P. J. Courtois. Decomposability; Queuing and Computer System Applications. Academic Press, Orlando, Florida, 1977.Google Scholar
  3. 3.
    P.J. Courtois and P. Semal, Bounds for the positive eigenvectors of nonnegative matrices and their approximation by decomposition. J. Assoc. Comp. Mach. 31 (1984), 804–825.Google Scholar
  4. 4.
    R. Koury, D.F. McAllister and W.J. Stewart. Methods for computing stationary distributions of NCD Markov chains. SIAM J. Alg. Disc. Math. 5, 2 (1984), 164–186.Google Scholar
  5. 5.
    P.J. Schweitzer. Aggregation methods for large Markov chains. International Workshop oh Applied Mathematics and Performance Reliability Models of Computer Communication Systems. University of Pisa, Italy, (1983) 225–234.Google Scholar
  6. 6.
    W.J. Stewart and A. Touzene. On Solving coupling Matrices arising in Iterative Aggregation/Disagregation Methods. In proceedings of International Workshop on Modeling, Analysis and Simulation of Computer and Telecommunication Systems (MASCOTS '94), Durham, USA, January 1994.Google Scholar
  7. 7.
    W.J. Stewart and W. Wu. Numerical Experiments with Iteration and Aggregation for Markov Chains. ORSA Journal on Computing, July–August, 1992.Google Scholar
  8. 8.
    E.Gelenbe J. Labetoulle R. Marie and W. J. Stewart. Reseaux de files d'attentes — modelisation et traitement numerique. Ed. des hommes et technique de l'AFCET, 1980.Google Scholar
  9. 9.
    R. S. Varga. Matrix Iteratives Analysis. Prentice Hall, Englewood Cliffs, N.J., 1963.Google Scholar
  10. 10.
    Y. Saad. Krylov Subspace Methods for Solving Unsymetric Linear Systems. Mathematics of Computation, 37, 105–126.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1995

Authors and Affiliations

  • Abderezak Touzene
    • 1
  1. 1.College of Computer Science and Information Sciences Department of Computer ScienceKing Saud UniversityRiyadhSaudi Arabia

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