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Article: Efficient parallel algorithm for dense matrix LU decomposition with pivoting on hypercubes

TitleEfficient parallel algorithm for dense matrix LU decomposition with pivoting on hypercubes
Authors
KeywordsEfficiency of parallel algorithms
Hypercubes
Linear systems of equations
LU decomposition
Parallel processing
Partial pivoting
Issue Date1997
PublisherPergamon. The Journal's web site is located at http://www.elsevier.com/locate/camwa
Citation
Computers And Mathematics With Applications, 1997, v. 33 n. 8, p. 39-50 How to Cite?
AbstractLU decomposition is intensively used in various scientific and engineering computations. A parallel algorithm for dense matrix LU decomposition with pivoting on hypercubes is presented. Using n processors, the presented algorithm can finish LU decomposition of an n x n matrix in O(n2/3 + O(n√nlog2 n)) steps, including computations as well as communications, and its efficiency is 1 asymptotically when n becomes large. The algorithm employs row-column-as well as block-parallelisms interchangeably so that the n processors are used efficiently in the whole computation process. Using the rich connectivity, all the data alignment requirements can be realized in O(log2 n) steps. The algorithm proposed here not only is suitable for systems with small numbers of processors, but also is suitable for systems with large numbers of processors.
Persistent Identifierhttp://hdl.handle.net/10722/89117
ISSN
2015 Impact Factor: 1.398
2015 SCImago Journal Rankings: 1.092
References

 

DC FieldValueLanguage
dc.contributor.authorLiu, Zen_HK
dc.contributor.authorCheung, DWen_HK
dc.date.accessioned2010-09-06T09:52:36Z-
dc.date.available2010-09-06T09:52:36Z-
dc.date.issued1997en_HK
dc.identifier.citationComputers And Mathematics With Applications, 1997, v. 33 n. 8, p. 39-50en_HK
dc.identifier.issn0898-1221en_HK
dc.identifier.urihttp://hdl.handle.net/10722/89117-
dc.description.abstractLU decomposition is intensively used in various scientific and engineering computations. A parallel algorithm for dense matrix LU decomposition with pivoting on hypercubes is presented. Using n processors, the presented algorithm can finish LU decomposition of an n x n matrix in O(n2/3 + O(n√nlog2 n)) steps, including computations as well as communications, and its efficiency is 1 asymptotically when n becomes large. The algorithm employs row-column-as well as block-parallelisms interchangeably so that the n processors are used efficiently in the whole computation process. Using the rich connectivity, all the data alignment requirements can be realized in O(log2 n) steps. The algorithm proposed here not only is suitable for systems with small numbers of processors, but also is suitable for systems with large numbers of processors.en_HK
dc.languageengen_HK
dc.publisherPergamon. The Journal's web site is located at http://www.elsevier.com/locate/camwaen_HK
dc.relation.ispartofComputers and Mathematics with Applicationsen_HK
dc.subjectEfficiency of parallel algorithmsen_HK
dc.subjectHypercubesen_HK
dc.subjectLinear systems of equationsen_HK
dc.subjectLU decompositionen_HK
dc.subjectParallel processingen_HK
dc.subjectPartial pivotingen_HK
dc.titleEfficient parallel algorithm for dense matrix LU decomposition with pivoting on hypercubesen_HK
dc.typeArticleen_HK
dc.identifier.openurlhttp://library.hku.hk:4550/resserv?sid=HKU:IR&issn=0898-1221&volume=33 No 8&spage=&epage=&date=1997&atitle=Efficient+Parallel+Algorithm+for+Dense+Matrix+LU+Decomposition+with+Pivoting+on+Hypercubesen_HK
dc.identifier.emailCheung, DW:dcheung@cs.hku.hken_HK
dc.identifier.authorityCheung, DW=rp00101en_HK
dc.description.naturelink_to_subscribed_fulltext-
dc.identifier.scopuseid_2-s2.0-0031123707en_HK
dc.identifier.hkuros26182en_HK
dc.relation.referenceshttp://www.scopus.com/mlt/select.url?eid=2-s2.0-0031123707&selection=ref&src=s&origin=recordpageen_HK
dc.identifier.volume33en_HK
dc.identifier.issue8en_HK
dc.identifier.spage39en_HK
dc.identifier.epage50en_HK
dc.publisher.placeUnited Kingdomen_HK
dc.identifier.scopusauthoridLiu, Z=7406671827en_HK
dc.identifier.scopusauthoridCheung, DW=34567902600en_HK

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