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1、COMPACTNUMERICALMETHODSFORCOMPUTERSlinearalgebraandfunctionminimisationSecondEditionJCNASHAdamHilger,BristolandNewYorkCopyright©1979,1990JCNashAllrightsreserved.Nopartofthispublicationmaybereproduced,storedinaretrievalsystemortransmittedinanyformorbyanyme
2、ans,electronic,mechanical,photocopyingorotherwise,withoutthepriorpermissionofthepublisher.MultiplecopyingisonlypermittedunderthetermsoftheagreementbetweentheCommitteeofVice-ChancellorsandPrincipalsandtheCopyrightLicensingAgency.BritishLibraryCataloguingin
3、PublicationDataNash,J.C.Compactnumericalmethodsforcomputers:linearalgebraandfunctionminimisation-2nded.1!.Numericalanalysis.Applicationsofmicrocomputer&minicomputersystems.AlgorithmsI.Title519.4ISBN0-85274-318-1ISBN0-85274-319-X(pbk)ISBN0-7503-0036-1(5¼"I
4、BMdisc)ISBN0-7503-0043-4(3½"IBMdisc)LibraryofCongressCataloging-in-PublicationDataareavailableFirstpublished,1979Reprinted,1980Secondedition,1990PublishedundertheAdamHilgerimprintbyIOPPublishingLtdTechnoHouse,RedcliffeWay,BristolBSl6NX,England335East45thS
5、treet,NewYork,NY10017-3483,USAFilmsetbyBathTypesettingLtd,Bath,AvonPrintedinGreatBritainbyPageBros(Norwich)LtdCONTENTSPrefacetotheSecondEditionixPrefacetotheFirstEditionxi1.ASTARTINGPOINT11.1.Purposeandscope11.2.Machinecharacteristics31.3.Sourcesofprogram
6、s91.4.Programminglanguagesusedandstructuredprogramming111.5.Choiceofalgorithms131.6.Amethodforexpressingalgorithms151.7.Generalnotation171.8.Softwareengineeringissues172.FORMALPROBLEMSINLINEARALGEBRA192.1.Introduction192.2.Simultaneouslinearequations192.3
7、.Thelinearleast-squaresproblem212.4.Theinverseandgeneralisedinverseofamatrix242.5.Decompositionsofamatrix262.6.Thematrixeigenvalueproblem283.THESINGULAR-VALUEDECOMPOSITIONANDITSUSETOSOLVELEAST-SQUARESPROBLEMS303.1.Introduction303.2.Asingular-valuedecompos
8、itionalgorithm313.3.Orthogonalisationbyplanerotations323.4.Afinepoint353.5.Analternativeimplementationofthesingular-valuedecomposi-tion383.6.Usingthesingular-valuedecompositiontosolveleast-squaresproblems404.HANDLIN
