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Article: Circulant approximation for preconditioning in stochastic automata networks

TitleCirculant approximation for preconditioning in stochastic automata networks
Authors
Issue Date2000
PublisherPergamon. The Journal's web site is located at http://www.elsevier.com/locate/camwa
Citation
Computers And Mathematics With Applications, 2000, v. 39 n. 3-4, p. 147-160 How to Cite?
AbstractStochastic 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.
Persistent Identifierhttp://hdl.handle.net/10722/75289
ISSN
2015 Impact Factor: 1.398
2015 SCImago Journal Rankings: 1.092
ISI Accession Number ID
References

 

DC FieldValueLanguage
dc.contributor.authorChing, WKen_HK
dc.contributor.authorZhou, XYen_HK
dc.date.accessioned2010-09-06T07:09:43Z-
dc.date.available2010-09-06T07:09:43Z-
dc.date.issued2000en_HK
dc.identifier.citationComputers And Mathematics With Applications, 2000, v. 39 n. 3-4, p. 147-160en_HK
dc.identifier.issn0898-1221en_HK
dc.identifier.urihttp://hdl.handle.net/10722/75289-
dc.description.abstractStochastic 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.en_HK
dc.languageengen_HK
dc.publisherPergamon. The Journal's web site is located at http://www.elsevier.com/locate/camwaen_HK
dc.relation.ispartofComputers and Mathematics with Applicationsen_HK
dc.titleCirculant approximation for preconditioning in stochastic automata networksen_HK
dc.typeArticleen_HK
dc.identifier.openurlhttp://library.hku.hk:4550/resserv?sid=HKU:IR&issn=0898-1221&volume=39&spage=147&epage=160&date=2000&atitle=Circulant+Approximation+for+Preconditioning+in+Stochastic+Automata+Networksen_HK
dc.identifier.emailChing, WK:wching@hku.hken_HK
dc.identifier.authorityChing, WK=rp00679en_HK
dc.description.naturelink_to_subscribed_fulltext-
dc.identifier.doi10.1016/S0898-1221(99)00341-7en_HK
dc.identifier.scopuseid_2-s2.0-0034140281en_HK
dc.identifier.hkuros63210en_HK
dc.relation.referenceshttp://www.scopus.com/mlt/select.url?eid=2-s2.0-0034140281&selection=ref&src=s&origin=recordpageen_HK
dc.identifier.volume39en_HK
dc.identifier.issue3-4en_HK
dc.identifier.spage147en_HK
dc.identifier.epage160en_HK
dc.identifier.isiWOS:000085203800014-
dc.publisher.placeUnited Kingdomen_HK
dc.identifier.scopusauthoridChing, WK=13310265500en_HK
dc.identifier.scopusauthoridZhou, XY=7410089984en_HK

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