Block SOR for Kronecker structured representations
dc.citation.epage | 109 | en_US |
dc.citation.issueNumber | Special Issue on the Conference on the Numerical Solution of Markov Chains 2003 | en_US |
dc.citation.spage | 83 | en_US |
dc.citation.volumeNumber | 386 | en_US |
dc.contributor.author | Buchholz, P. | en_US |
dc.contributor.author | Dayar, Tuğrul | en_US |
dc.coverage.spatial | Urbana-Champaign, IL, USA | en_US |
dc.date.accessioned | 2016-02-08T11:53:57Z | |
dc.date.available | 2016-02-08T11:53:57Z | en_US |
dc.date.issued | 2004 | en_US |
dc.department | Department of Computer Engineering | en_US |
dc.description | Conference name: Conference on the Numerical Solution of Markov Chains 2003 | en_US |
dc.description | Date of Conference: 3-5 September 2003 | en_US |
dc.description.abstract | The 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.description.provenance | Made available in DSpace on 2016-02-08T11:53:57Z (GMT). No. of bitstreams: 1 bilkent-research-paper.pdf: 70227 bytes, checksum: 26e812c6f5156f83f0e77b261a471b5a (MD5) Previous issue date: 2004 | en_US |
dc.identifier.doi | 10.1016/j.laa.2003.12.017 | en_US |
dc.identifier.issn | 0024-3795 | en_US |
dc.identifier.uri | http://hdl.handle.net/11693/27455 | en_US |
dc.language.iso | English | en_US |
dc.publisher | Elsevier | en_US |
dc.relation.isversionof | http://dx.doi.org/10.1016/j.laa.2003.12.017 | en_US |
dc.source.title | Linear Algebra and Its Applications | en_US |
dc.subject | Block SOR | en_US |
dc.subject | COLAMD ordering | en_US |
dc.subject | Kronecker based numerical techniques | en_US |
dc.subject | Markov chains | en_US |
dc.subject | Real Schur factorization | en_US |
dc.subject | Algorithms | en_US |
dc.subject | Approximation theory | en_US |
dc.subject | Computation theory | en_US |
dc.subject | Computer simulation | en_US |
dc.subject | Mathematical models | en_US |
dc.subject | Matrix algebra | en_US |
dc.subject | Block SOR | en_US |
dc.subject | COLAMD ordering | en_US |
dc.subject | Kronecker based numerical techniques | en_US |
dc.subject | Real Schur factorization | en_US |
dc.subject | Markov processes | en_US |
dc.title | Block SOR for Kronecker structured representations | en_US |
dc.type | Conference Paper | en_US |
Files
Original bundle
1 - 1 of 1
Loading...
- Name:
- Block SOR for Kronecker structured representations.pdf
- Size:
- 273.53 KB
- Format:
- Adobe Portable Document Format
- Description:
- Full printable version