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1、ParallelNumericalLinearAlgebraJamesW.DemmelyMichaelT.HeathzHenkA.vanderVorstOctober6,1992AbstractWesurveygeneraltechniquesandopenproblemsinnumericallinearalgebraonparallelarchitectures.We rstdiscussbasicprinciplesofparallelprocessing,describingthecostsofbasicoperati
2、onsonparallelmachines,includinggeneralprinciplesforcon-structingecientalgorithms.Weillustratetheseprinciplesusingcurrentarchitecturesandsoftwaresystems,andbyshowinghowonewouldimplementmatrixmultiplication.Then,wepresentdirectanditerativealgorithmsforsolvinglinearsys
3、temsofequations,linearleastsquaresproblems,thesymmetriceigenvalueproblem,thenonsymmetriceigenvalueproblem,thesingularvaluedecomposition,andgeneralizationsofthesetotwomatrices.Weconsiderdense,bandandsparsematrices.ToappearinActaNumerica,CambridgeUniversityPressCompute
4、rScienceDivisionTechReportUCB//CSD-92-703,U.C.Berkeley,October1992ComputerScienceDivisionandMathematicsDepartment,UniversityofCalifornia,BerkeleyCA94720.TheauthorwassupportedbyNSFgrantASC-9005933,DARPAcontractDAAL03-91-C-0047viaasub-contractfromtheUniversityofTennes
5、see(administeredbyARO),andDARPAgrantDM28E04120viaasubcontractfromArgonneNationalLaboratory.ThisworkwaspartiallyperformedduringavisittotheInstituteforMathematicsanditsApplicationsattheUniversityofMinnesota.yDepartmentofComputerScienceandNationalCenterforSupercomputing
6、Applications,UniversityofIllinois,405N.MathewsAve.,Urbana,IL61801.TheauthorwassupportedbyDARPAcontractDAAL03-91-C-0047viaasubcontractfromtheUniversityofTennessee,andadministeredbyARO.zMathematicalInstitute,UtrechtUniversity,P.O.Box80.010,NL-3508TAUtrecht,theNetherlan
7、ds.ThisworkwassupportedinpartbyaNCF/CrayResearchUniversityGrantCRG92.03.1Contents1Introduction42FeaturesofParallelSystems52.1GeneralPrinciples::::::::::::::::::::::::::::::::52.2Examples:::::::::::::::::::::::::::::::::::::62.3ImportantTradeo s:::::::::::::::::::::::
8、::::::::123MatrixMultiplication133.1Matrixmultiplicationonasharedmemorymachine::::::::::::::143.2Matrixmultiplicationonadistributed
