State space orderings for Gauss-Seidel in Markov chains revisited

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dc.citation.epage154en_US
dc.citation.issueNumber1en_US
dc.citation.spage148en_US
dc.citation.volumeNumber19en_US
dc.contributor.authorDayar, Tuğrulen_US
dc.date.accessioned2016-02-08T10:46:07Z
dc.date.available2016-02-08T10:46:07Zen_US
dc.date.issued1998en_US
dc.departmentDepartment of Computer Engineeringen_US
dc.description.abstractStates of a Markov chain may be reordered to reduce the magnitude of the subdominant eigenvalue of the Gauss-Seidel (GS) iteration matrix. Orderings that maximize the elemental mass or the number of nonzero elements in the dominant term of the GS splitting (that is, the term approximating the coefficient matrix) do not necessarily converge faster. An ordering of a Markov chain that satisfies Property-R is semiconvergent. On the other hand, there are semiconvergent state space orderings that do not satisfy Property-R. For a given ordering, a simple approach for checking Property-R is shown. Moreover, a version of the Cuthill-McKee algorithm may be used to order the states of a Markov chain so that Property-R is satisfied. The computational complexity of the ordering algorithm is less than that of a single GS iteration. In doing all this, the aim is to gain insight into (faster) converging orderings.en_US
dc.description.provenanceMade available in DSpace on 2016-02-08T10:46:07Z (GMT). No. of bitstreams: 1 bilkent-research-paper.pdf: 70227 bytes, checksum: 26e812c6f5156f83f0e77b261a471b5a (MD5) Previous issue date: 1998en_US
dc.identifier.doi10.1137/S1064827596303612en_US
dc.identifier.eissn1095-7197
dc.identifier.issn1064-8275
dc.identifier.urihttp://hdl.handle.net/11693/25517en_US
dc.language.isoEnglishen_US
dc.publisherSIAMen_US
dc.relation.isversionofhttps://doi.org/10.1137/S1064827596303612en_US
dc.source.titleSIAM Journal on Scientific Computingen_US
dc.subjectCuthill-Mckee Algorithmen_US
dc.subjectGauss-Seidelen_US
dc.subjectMarkov Chainsen_US
dc.subjectProperty-Ren_US
dc.subjectState Space Orderingen_US
dc.titleState space orderings for Gauss-Seidel in Markov chains revisiteden_US
dc.typeArticleen_US

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