Block SOR for Kronecker structured representations

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dc.citation.epage109en_US
dc.citation.issueNumberSpecial Issue on the Conference on the Numerical Solution of Markov Chains 2003en_US
dc.citation.spage83en_US
dc.citation.volumeNumber386en_US
dc.contributor.authorBuchholz, P.en_US
dc.contributor.authorDayar, Tuğrulen_US
dc.coverage.spatialUrbana-Champaign, IL, USAen_US
dc.date.accessioned2016-02-08T11:53:57Z
dc.date.available2016-02-08T11:53:57Zen_US
dc.date.issued2004en_US
dc.departmentDepartment of Computer Engineeringen_US
dc.descriptionConference name: Conference on the Numerical Solution of Markov Chains 2003en_US
dc.descriptionDate of Conference: 3-5 September 2003en_US
dc.description.abstractThe Kronecker structure of a hierarchical Markovian model (HMM) induces nested block partitionings in the transition matrix of its underlying Markov chain. This paper shows how sparse real Schur factors of certain diagonal blocks of a given partitioning induced by the Kronecker structure can be constructed from smaller component matrices and their real Schur factors. Furthermore, it shows how the column approximate minimum degree (COLAMD) ordering algorithm can be used to reduce fill-in of the remaining diagonal blocks that are sparse LU factorized. Combining these ideas, the paper proposes three-level block successive over-relaxation (BSOR) as a competitive steady state solver for HMMs. Finally, on a set of numerical experiments it demonstrates how these ideas reduce storage required by the factors of the diagonal blocks and improve solution time compared to an all LU factorization implementation of the BSOR solver. © 2004 Elsevier Inc. All rights reserved.en_US
dc.identifier.doi10.1016/j.laa.2003.12.017en_US
dc.identifier.issn0024-3795
dc.identifier.urihttp://hdl.handle.net/11693/27455en_US
dc.language.isoEnglishen_US
dc.publisherElsevieren_US
dc.relation.isversionofhttp://dx.doi.org/10.1016/j.laa.2003.12.017en_US
dc.source.titleLinear Algebra and Its Applicationsen_US
dc.subjectBlock SORen_US
dc.subjectCOLAMD orderingen_US
dc.subjectKronecker based numerical techniquesen_US
dc.subjectMarkov chainsen_US
dc.subjectReal Schur factorizationen_US
dc.subjectAlgorithmsen_US
dc.subjectApproximation theoryen_US
dc.subjectComputation theoryen_US
dc.subjectComputer simulationen_US
dc.subjectMathematical modelsen_US
dc.subjectMatrix algebraen_US
dc.subjectBlock SORen_US
dc.subjectCOLAMD orderingen_US
dc.subjectKronecker based numerical techniquesen_US
dc.subjectReal Schur factorizationen_US
dc.subjectMarkov processesen_US
dc.titleBlock SOR for Kronecker structured representationsen_US
dc.typeConference Paperen_US

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