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dc.contributor.authorBuchholz, Peteren_US
dc.contributor.authorDayar, Tuğrulen_US
dc.date.accessioned2016-02-08T10:22:21Z
dc.date.available2016-02-08T10:22:21Zen_US
dc.date.issued2005en_US
dc.identifier.issn1064-8275
dc.identifier.issn1095-7197
dc.identifier.urihttp://hdl.handle.net/11693/23986en_US
dc.description.abstractKronecker structured representations are used to cope with the state space explosion problem in Markovian modeling and analysis. Currently, an open research problem is that of devising strong preconditioners to be used with projection methods for the computation of the stationary vector of Markov chains (MCs) underlying such representations. This paper proposes a block successive overrelaxation (BSOR) preconditioner for hierarchical Markovian models (HMMs1) that are composed of multiple low-level models and a high-level model that defines the interaction among low-level models. The Kronecker structure of an HMM yields nested block partitionings in its underlying continuous-time MC which may be used in the BSOR preconditioner. The computation of the BSOR preconditioned residual in each iteration of a preconditioned projection method becomes the problem of solving multiple nonsingular linear systems whose coefficient matrices are the diagonal blocks of the chosen partitioning. The proposed BSOR preconditioner solves these systems using sparse LU or real Schur factors of diagonal blocks. The fill-in of sparse LU factorized diagonal blocks is reduced using the column approximate minimum degree (COLAMD) ordering. A set of numerical experiments is presented to show the merits of the proposed BSOR preconditioner.en_US
dc.language.isoEnglishen_US
dc.source.titleSIAM Journal on Scientific Computingen_US
dc.relation.isversionofhttp://dx.doi.org/10.1137/S1064827503425882en_US
dc.subjectBlock SORen_US
dc.subjectCOLAMD orderingen_US
dc.subjectKronecker structured numerical techniquesen_US
dc.subjectMarkov chainsen_US
dc.subjectPreconditioningen_US
dc.subjectProjection methodsen_US
dc.subjectReal Schur factorizationen_US
dc.subjectBlock SORen_US
dc.subjectCOLAMD orderingen_US
dc.subjectKronecker structured numerical techniquesen_US
dc.subjectPreconditioningen_US
dc.subjectProjection methodsen_US
dc.subjectMathematical modelsen_US
dc.subjectNumerical methodsen_US
dc.subjectVectorsen_US
dc.subjectMarkov processesen_US
dc.titleBlock SOR preconditioned projection methods for Kronecker structured Markovian representationsen_US
dc.typeArticleen_US
dc.departmentDepartment of Computer Engineeringen_US
dc.citation.spage1289en_US
dc.citation.epage1313en_US
dc.citation.volumeNumber26en_US
dc.citation.issueNumber4en_US
dc.identifier.doi10.1137/S1064827503425882en_US
dc.publisherSIAMen_US


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