资源描述：
《factorization (rrqrf)》由会员上传分享，免费在线阅读，更多相关内容在教育资源-天天文库。
1、ABLAS-3VERSIONOFTHEQRFACTORIZATIONWITHCOLUMNPIVOTINGyzxGREGORIOQUINTANA-ORT,XIAOBAISUN,ANDCHRISTIANH.BISCHOFAbstract.TheQRfactorizationwithcolumnpivoting(QRP),originallysuggestedbyGolubandBusingerin1965,isapopularapproachtocomputingrank-revealingfactorizations.ItwasimplementedinLIN
2、PACKwiththeLevel1BLASandinLAPACKwiththeLevel2BLAS.WhiletheLevel2BLASversiongenerallydeliverssuperiorperformance,itmayresultinworseperformanceforlargematrixsizesduetocachee ects.Weintroduceamodi cationoftheQRPalgorithmthatallowstheuseofLevel3BLASkernelswhilemaintainingthenumericalbehav
3、ioroftheLINPACKandLAPACKimplementations.ExperimentalcomparisonsofthisapproachwiththeLINPACKandLAPACKimplementationsonIBMRS/6000,SGIR8000,andDECAlphaplatformsshowconsiderableperformanceimprovements.Keywords.QRFactorization,ColumnPivoting,RankRevealingFactorization,BlockAlgo-rithm1.Intr
4、oduction.ForanymatrixA,thereexistsaso-calledrank-revealingQRfactorization(RRQRF)RR1112(1)AP=QR=(QQ);120R22wherePisapermutationmatrix,Risuppertriangular,andRisnumerically1122negligible[22].TheorderrofRthenrevealsthenumericalrankofA.The rst11rcolumnsofQformanorthonormalbasisfortherang
5、espaceofA,andthe rstrcolumnsofAParethelargestindependentsetofcolumnsofA.Thisinformationisneeded,forexample,ingeodesy[17],computer-aideddesign[19],nonlinearleast-squaresproblems[25],thesolutionofintegralequations[15],andthecalculationofsplines[18].Otherapplicationsariseinbeam-forming[8
6、],spectralestimation[23],regularization[21,29],andeigenproblems[3].Algorithmsforthereliablecomputationofrank-revealingfactorizationshavere-centlyreceivedconsiderableattention(see,forexample[6,7,10,11,20,26,27]).However,themostcommonapproachtocomputingsuchanRRQRFisthecolumn-pivotingpro
7、ceduresuggestedbyBusingerandGolub[9].ThisQRfactorizationwithcolumnpivoting(QRP)mayfailtorevealthenumericalrankcorrectly,butitiswidelyusedbecauseofitssimplicityandpracticalreliability.Thus,itisalsoaveryusefulpreprocessingstepforthemorereliable(andmoreexpensive)RRQRFalgorithms.Allautho
8、rswer
