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Numerical Methods for Structured Markov Chains$
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Dario A. Bini, Guy Latouche, and Beatrice Meini

Print publication date: 2005

Print ISBN-13: 9780198527688

Published to Oxford Scholarship Online: September 2007

DOI: 10.1093/acprof:oso/9780198527688.001.0001

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ALTERNATIVE APPROACHES

ALTERNATIVE APPROACHES

Chapter:
(p.229) 8 ALTERNATIVE APPROACHES
Source:
Numerical Methods for Structured Markov Chains
Author(s):

D. A. Bini

G. Latouche

B. Meini

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780198527688.003.0008

Alternative numerical approaches for solving matrix equations associated with M/G/1-type Markov chains are considered in this chapter. A general shift technique for accelerating the convergence of iterative methods is described, and its application to accelerating cyclic reduction is analysed. A functional iteration relying on the combination of cyclic reduction and fixed point iteration is introduced: its convergence is linear but its convergence rate can be arbitrarily large. A doubling method, evaluation interpolation techniques, and the invariant subspace method complete the chapter.

Keywords:   shift technique, iterative methods, convergence acceleration, cyclic reduction, fixed point iteration, doubling method, evaluation interpolation, invariant subspace method

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