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Article: Gradient-based maximal convergence rate iterative method for solving linear matrix equations

TitleGradient-based maximal convergence rate iterative method for solving linear matrix equations
Authors
KeywordsDiscrete-Time Linear System Theory
Gradient-Based Iterative Algorithm
Lyapunov Matrix Equations
Numerical Computing
Sylvester Matrix Equations
Issue Date2010
PublisherTaylor & Francis Ltd. The Journal's web site is located at http://www.tandf.co.uk/journals/titles/00207160.asp
Citation
International Journal Of Computer Mathematics, 2010, v. 87 n. 3, p. 515-527 How to Cite?
AbstractThis paper is concerned with numerical solutions to general linear matrix equations including the well-known Lyapunov matrix equation and Sylvester matrix equation as special cases. Gradient based iterative algorithm is proposed to approximate the exact solution. A necessary and sufficient condition guaranteeing the convergence of the algorithm is presented. A sufficient condition that is easy to compute is also given. The optimal convergence factor such that the convergence rate of the algorithm is maximized is established. The proposed approach not only gives a complete understanding on gradient based iterative algorithm for solving linear matrix equations, but can also be served as a bridge between linear system theory and numerical computing. Numerical example shows the effectiveness of the proposed approach.
Persistent Identifierhttp://hdl.handle.net/10722/157050
ISSN
2015 Impact Factor: 0.577
2015 SCImago Journal Rankings: 0.474
ISI Accession Number ID
References

 

DC FieldValueLanguage
dc.contributor.authorZhou, Ben_US
dc.contributor.authorLam, Jen_US
dc.contributor.authorDuan, GRen_US
dc.date.accessioned2012-08-08T08:45:06Z-
dc.date.available2012-08-08T08:45:06Z-
dc.date.issued2010en_US
dc.identifier.citationInternational Journal Of Computer Mathematics, 2010, v. 87 n. 3, p. 515-527en_US
dc.identifier.issn0020-7160en_US
dc.identifier.urihttp://hdl.handle.net/10722/157050-
dc.description.abstractThis paper is concerned with numerical solutions to general linear matrix equations including the well-known Lyapunov matrix equation and Sylvester matrix equation as special cases. Gradient based iterative algorithm is proposed to approximate the exact solution. A necessary and sufficient condition guaranteeing the convergence of the algorithm is presented. A sufficient condition that is easy to compute is also given. The optimal convergence factor such that the convergence rate of the algorithm is maximized is established. The proposed approach not only gives a complete understanding on gradient based iterative algorithm for solving linear matrix equations, but can also be served as a bridge between linear system theory and numerical computing. Numerical example shows the effectiveness of the proposed approach.en_US
dc.languageengen_US
dc.publisherTaylor & Francis Ltd. The Journal's web site is located at http://www.tandf.co.uk/journals/titles/00207160.aspen_US
dc.relation.ispartofInternational Journal of Computer Mathematicsen_US
dc.subjectDiscrete-Time Linear System Theoryen_US
dc.subjectGradient-Based Iterative Algorithmen_US
dc.subjectLyapunov Matrix Equationsen_US
dc.subjectNumerical Computingen_US
dc.subjectSylvester Matrix Equationsen_US
dc.titleGradient-based maximal convergence rate iterative method for solving linear matrix equationsen_US
dc.typeArticleen_US
dc.identifier.emailLam, J:james.lam@hku.hken_US
dc.identifier.authorityLam, J=rp00133en_US
dc.description.naturelink_to_subscribed_fulltexten_US
dc.identifier.doi10.1080/00207160802123458en_US
dc.identifier.scopuseid_2-s2.0-74949106570en_US
dc.identifier.hkuros179611-
dc.relation.referenceshttp://www.scopus.com/mlt/select.url?eid=2-s2.0-74949106570&selection=ref&src=s&origin=recordpageen_US
dc.identifier.volume87en_US
dc.identifier.issue3en_US
dc.identifier.spage515en_US
dc.identifier.epage527en_US
dc.identifier.isiWOS:000273011900004-
dc.publisher.placeUnited Kingdomen_US
dc.identifier.scopusauthoridZhou, B=7401906664en_US
dc.identifier.scopusauthoridLam, J=7201973414en_US
dc.identifier.scopusauthoridDuan, GR=35229183800en_US

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