Circulant preconditioners for stochastic automata networks


Chan, Raymond H. and Ching, Wai Ki (2000) Circulant preconditioners for stochastic automata networks. Numerische Mathematik, 87, (1), 35-57. (doi:10.1007/s002110000173).

Download

Full text not available from this repository.

Original Publication URL: http://dx.doi.org/10.1007/s002110000173

Description/Abstract

Stochastic Automata Networks (SANs) are widely used in modeling communication systems, manufacturing systems and computer systems. The SAN approach gives a more compact and efficient representation of the network when compared to the stochastic Petri nets approach. To find the steady state distribution of SANs, it requires solutions of linear systems involving the generator matrices of the SANs. Very often, direct methods such as the LU decomposition are inefficient because of the huge size of the generator matrices. An efficient algorithm should make use of the structure of the matrices. Iterative methods such as the conjugate gradient methods are possible choices. However, their convergence rates are slow in general and preconditioning is required. We note that the MILU and MINV based preconditioners are not appropriate because of their expensive construction cost. In this paper, we consider preconditioners obtained by circulant approximations of SANs. They have low construction cost and can be inverted efficiently. We prove that if only one of the automata is large in size compared to the others, then the preconditioned system of the normal equations will converge very fast. Numerical results for three different SANs solved by CGS are given to illustrate the fast convergence of our method.

Item Type: Article
ISSNs: 0029-599X (print)
Related URLs:
Subjects: Q Science > QA Mathematics
Divisions: University Structure - Pre August 2011 > School of Mathematics > Operational Research
ePrint ID: 29749
Date Deposited: 20 Jul 2006
Last Modified: 27 Mar 2014 18:18
URI: http://eprints.soton.ac.uk/id/eprint/29749

Actions (login required)

View Item View Item