Circulant approximation for preconditioning in stochastic automata networks

Ching, Wai Ki and Zhou, Xun Yu (2000) Circulant approximation for preconditioning in stochastic automata networks. Computers and Mathematics with Applications, 39, (3-4), 147-160. (doi:10.1016/S0898-1221(99)00341-7).


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Stochastic Automata Networks (SANs) are widely used in modeling practical systems such as queueing systems, communication systems, and manufacturing systems. For the performance analysis purposes, one needs to calculate the steady-state distributions of SANs. Usually, the steady-state distributions have no close form solutions and cannot be obtained efficiently by direct methods such as LU decomposition due to the huge size of the generator matrices. An efficient numerical method should make use of the tensor structure of SANs' generator matrices. The generalized Conjugate Gradient (CG) methods are possible choices though their convergence rates are slow in general. To speed up the convergence rate, preconditioned CG methods are considered in this paper. In particular, circulant based preconditioners for the SANs are constructed. The preconditioners presented in this paper are easy to construct and can be inverted efficiently. Numerical examples of practical SANs are also given to illustrate the fast convergence rate of the method.

Item Type: Article
Digital Object Identifier (DOI): doi:10.1016/S0898-1221(99)00341-7
ISSNs: 0898-1221 (print)
Related URLs:
Keywords: stochastic automata networks, steady-state distributions, circulant approximation, preconditioners, conjugate gradient methods
Subjects: Q Science > QA Mathematics > QA75 Electronic computers. Computer science
Q Science > QA Mathematics
Divisions : University Structure - Pre August 2011 > School of Mathematics > Operational Research
ePrint ID: 29748
Accepted Date and Publication Date:
Date Deposited: 20 Jul 2006
Last Modified: 31 Mar 2016 11:55

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