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1、COMPACTNUMERICALMETHODSFORCOMPUTERSlinearalgebraandfunctionminimisationSecondEditionJCNASHAdamHilger,BristolandNewYorkCopyright©1979,1990JCNashAllrightsreserved.Nopartofthispublicationmaybereproduced,storedinaretrievalsystemortransmittedinanyformorbyanymeans,electronic,mechanical,photocopyingorother
2、wise,withoutthepriorpermissionofthepublisher.MultiplecopyingisonlypermittedunderthetermsoftheagreementbetweentheCommitteeofVice-ChancellorsandPrincipalsandtheCopyrightLicensingAgency.BritishLibraryCataloguinginPublicationDataNash,J.C.Compactnumericalmethodsforcomputers:linearalgebraandfunctionminimi
3、sation-2nded.1!.Numericalanalysis.Applicationsofmicrocomputer&minicomputersystems.AlgorithmsI.Title519.4ISBN0-85274-318-1ISBN0-85274-319-X(pbk)ISBN0-7503-0036-1(5¼"IBMdisc)ISBN0-7503-0043-4(3½"IBMdisc)LibraryofCongressCataloging-in-PublicationDataareavailableFirstpublished,1979Reprinted,1980Seconded
4、ition,1990PublishedundertheAdamHilgerimprintbyIOPPublishingLtdTechnoHouse,RedcliffeWay,BristolBSl6NX,England335East45thStreet,NewYork,NY10017-3483,USAFilmsetbyBathTypesettingLtd,Bath,AvonPrintedinGreatBritainbyPageBros(Norwich)LtdCONTENTSPrefacetotheSecondEditionixPrefacetotheFirstEditionxi1.ASTARTI
5、NGPOINT11.1.Purposeandscope11.2.Machinecharacteristics31.3.Sourcesofprograms91.4.Programminglanguagesusedandstructuredprogramming111.5.Choiceofalgorithms131.6.Amethodforexpressingalgorithms151.7.Generalnotation171.8.Softwareengineeringissues172.FORMALPROBLEMSINLINEARALGEBRA192.1.Introduction192.2.Si
6、multaneouslinearequations192.3.Thelinearleast-squaresproblem212.4.Theinverseandgeneralisedinverseofamatrix242.5.Decompositionsofamatrix262.6.Thematrixeigenvalueproblem283.THESINGULAR-VALUEDECOMPOSITIONANDITSUSETOSOLVELEAST-SQUARESPROBLEMS303.1.Introduction303.2.Asingular-valuedecompositionalgorithm3
7、13.3.Orthogonalisationbyplanerotations323.4.Afinepoint353.5.Analternativeimplementationofthesingular-valuedecomposi-tion383.6.Usingthesingular-valuedecompositiontosolveleast-squaresproblems404.HANDLIN
