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dc.contributor.authorDayar T.en_US
dc.contributor.authorStewart, W. J.en_US
dc.date.accessioned2016-02-08T10:38:36Z
dc.date.available2016-02-08T10:38:36Zen_US
dc.date.issued2000en_US
dc.identifier.issn1064-8275
dc.identifier.issn1095-7197
dc.identifier.urihttp://hdl.handle.net/11693/25062en_US
dc.description.abstractExperimental results for large, sparse Markov chains, especially the ill-conditioned nearly completely decomposable (NCD) ones, are few. We believe there is need for further research in this area, specifically to aid in the understanding of the effects of the degree of coupling of NCD Markov chains and their nonzero structure on the convergence characteristics and space requirements of iterative solvers. The work of several researchers has raised the following questions that led to research in a related direction: How must one go about partitioning the global coefficient matrix into blocks when the system is NCD and a two-level iterative solver (such as block SOR) is to be employed? Are block partitionings dictated by the NCD form of the stochastic one-step transition probability matrix necessarily superior to others? Is it worth investigating alternative partitionings? Better yet, for a fixed labeling and partitioning of the states, how does the performance of block SOR (or even that of point SOR) compare to the performance of the iterative aggregation-disaggregation (IAD) algorithm? Finally, is there any merit in using two-level iterative solvers when preconditioned Krylov subspace methods are available? We seek answers to these questions on a test suite of 13 Markov chains arising in 7 applications.en_US
dc.language.isoEnglishen_US
dc.source.titleSIAM Journal on Scientific Computingen_US
dc.relation.isversionofhttps://doi.org/10.1137/S1064827598338159en_US
dc.subjectKrylov Subspace Methodsen_US
dc.subjectNear Complete Decomposabilityen_US
dc.subjectPartitioningen_US
dc.subjectTwo Level Iterative Solversen_US
dc.subjectAlgorithmsen_US
dc.subjectConstraint Theoryen_US
dc.subjectLinear Equationsen_US
dc.subjectMarkov Processesen_US
dc.subjectMatrix Algebraen_US
dc.subjectProblem Solvingen_US
dc.subjectVectorsen_US
dc.subjectIterative Methodsen_US
dc.titleComparison of partitioning techniques for two-level iterative solvers on large, sparse Markov chainsen_US
dc.typeArticleen_US
dc.departmentDepartment of Computer Engineeringen_US
dc.citation.spage1691en_US
dc.citation.epage1705en_US
dc.citation.volumeNumber21en_US
dc.citation.issueNumber5en_US
dc.identifier.doi10.1137/S1064827598338159en_US
dc.publisherSIAMen_US


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