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1、ISSN1360-1725UMISTParallelSingularValueDecompositionviathePolarDecompositionN.J.HighamandP.PapadimitriouNumericalAnalysisReportNo.239October1993ManchesterCentreforComputationalMathematicsNumericalAnalysisReportsDEPARTMENTSOFMATHEMATICSReportsavailablefrom:And
2、overtheWorld-WideWebfromURLsDepartmentofMathematicshttp://www.ma.man.ac.uk/MCCM/MCCM.htmlUniversityofManchesterftp://ftp.ma.man.ac.uk/pub/narepManchesterM139PLEnglandParallelSingularValueDecompositionviathePolarDecompositionyNicholasJ.HighamPythagorasPapadim
3、itriouOctober30,1993AbstractAnewmethodisdescribedforcomputingthesingularvaluedecomposition(SVD).ItbeginsbycomputingthepolardecompositionandthencomputesthespectraldecompositionoftheHermitianpolarfactor.Themethodisparticularlyattractiveforsharedmemoryparallelco
4、mputerswitharelativelysmallnumberofprocessors,becausethepolardecompositioncanbecomputedecientlyonsuchmachinesusinganiterativemethoddevelopedrecentlybytheauthors.Thisiter-ativepolardecompositionmethodrequiresonlymatrixmultiplicationandmatrixinversionkernelsfo
5、ritsimplementationandisdesignedforfullrankmatrices;thustheproposedSVDmethodisintendedformatricesthatarenottooclosetobeingrank-de cient.OntheKendallSquareKSR1virtualsharedmemorycomputerthenewmethodisuptosixtimesfasterthanaparallelizedversionoftheLAPACKSVDrouti
6、ne,dependingontheconditionnumberofthematrix.Keywords.singularvaluedecomposition,polardecomposition,numericalstability,LAPACK,level3BLAS,KendallSquareResearchKSR1computerAMSsubjectclassi cations.primary65F15DepartmentofMathematics,UniversityofManchester,Manch
7、ester,M139PL,England(na.nhigham@na-net.ornl.gov).TheworkofthisauthorwassupportedbyScienceandEngineer-ingResearchCouncilgrantGR/H52139,andbytheEECEspritBasicResearchActionProgramme,Project6634(APPARC).yDepartmentofMathematics,UniversityofManchester,Manchester,
8、M139PL,England(na.papadimitriou@na-net.ornl.gov).Currentaddress:DataInformationSystemsPLC,125Thes-salonikis,N.Philadelphia,Athens14243,Greece.ThisauthorwassupportedbyanSERCResearchStudent
