Proceedings of the 2003 conference on
The Numerical Solution of Markov Chains.
Urbana-Champaign, Illinois, USA.

Published as a Special Issue of
"Linear Algebra and its Applications",
Volume 386, 15 July 2004.

Edited by

Amy N. Langville and William J. Stewart

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Table of Contents

  1. Preface.
    A.N. Langville and W.J. Stewart ... 1

  2. The Life and work of A.A. Markov.
    G.P. Basharin, A.N. Langville and V.A. Naumov ... 3

  3. A direct project method for Markov chains.
    M. Benzi ... 27

  4. Adaptive methods for the computation of PageRank.
    S. Kamvar, T. Haveliwala and G. Golub ... 51

  5. Algebraic Schwarz methods for the numerical solution of Markov chains.
    I. Marek and D.B. Szyld ... 67

  6. Blokk SOR for Kronecker structured representations.
    P. Buchholz and T. Dayar ... 83

  7. Aggregation of stochastic automata with replicas.
    A. Benoit, L. Brenner, P. Fernandes and B. Plateau ... 111

  8. Symbolic state-space exploration and numerical analysis of state-sharing composed models.
    S. Derisavi, P. Kemper and W.H. Sanders ... 137

  9. Algorithms for an irreducible and lumpable strong stochastic bound.
    J-M. Fourneau, M. Lecoz and F. Quessette ... 167

  10. Non-skip-free M/G/1-type Markov chains and Laurent matrix power series.
    D.A. Bini and B. Meini ... 187

  11. Finding equilibrium probabilities of QBD processes by spectral methods when eigenvalues vanish.
    W.K. Grassmann ... 207

  12. Improved bounds for a condition number for Markov chains.
    M. Neumann and J. Xu ... 225

  13. The first Laurent series coefficients for singularly perturbed stochastic matrices.
    K.E. Avrachenkov and M. Haviv ... 243

  14. Rate-tilting for fast simulation of level/phase processes.
    J. Luo and W.K. Grassmann ... 261

  15. On the exact simulation of functional of stationary Markov chains.
    J-M. Vincent and C. Marchand ... 285

  16. Hypergraph-based parallel computation of passage times densities in large semi-Markov models.
    J.T. Bradley, N.T.Dingle, W.J. Knottenbelt and H.J. Wilson ... 311

  17. Approximate mean value analysis based on Markov chain aggregation by composition.
    D.C. Petriu and C.M. Woodside ... 335

  18. Reversed processes, product forms and a non-product form.
    P.G. Harrison ... 359

  19. Analysis of inhomogeneous Markov reward models.
    M. Telek, A. Horvath and G. Horvath ... 383

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