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Inexact uniformization method for computing transient distributions of Markov chains

Sidje, Roger, Burrage, Kevin, & Macnamara, Shev (2007) Inexact uniformization method for computing transient distributions of Markov chains. SIAM Journal on Scientific Computing, 29(6), pp. 2562-2580.

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Abstract

The uniformization method (also known as randomization) is a numerically stable algorithm for computing transient distributions of a continuous time Markov chain. When the solution is needed after a long run or when the convergence is slow, the uniformization method involves a large number of matrix-vector products. Despite this, the method remains very popular due to its ease of implementation and its reliability in many practical circumstances. Because calculating the matrix-vector product is the most time-consuming part of the method, overall efficiency in solving large-scale problems can be significantly enhanced if the matrix-vector product is made more economical. In this paper, we incorporate a new relaxation strategy into the uniformization method to compute the matrix-vector products only approximately. We analyze the error introduced by these inexact matrix-vector products and discuss strategies for refining the accuracy of the relaxation while reducing the execution cost. Numerical experiments drawn from computer systems and biological systems are given to show that significant computational savings are achieved in practical applications.

Impact and interest:

17 citations in Scopus
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14 citations in Web of Science®

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ID Code: 44312
Item Type: Journal Article
Keywords: Markov chains, uniformization, inexact methods, relaxed matrix-vector
DOI: 10.1137/060662629
ISSN: 1095-7197
Subjects: Australian and New Zealand Standard Research Classification > MATHEMATICAL SCIENCES (010000) > APPLIED MATHEMATICS (010200)
Australian and New Zealand Standard Research Classification > MATHEMATICAL SCIENCES (010000) > NUMERICAL AND COMPUTATIONAL MATHEMATICS (010300)
Australian and New Zealand Standard Research Classification > INFORMATION AND COMPUTING SCIENCES (080000) > COMPUTATION THEORY AND MATHEMATICS (080200)
Divisions: Past > QUT Faculties & Divisions > Faculty of Science and Technology
Deposited On: 25 Aug 2011 08:10
Last Modified: 01 Mar 2012 00:36

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