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1、undamentalsofMatrixComputationsSecondEditionPUREANDAPPLIEDMATHEMATICSAWiley-InterscienceSeriesofTexts,Monographs,andTractsFoundedbyRICHARDCOURANTEditors:MYRONB.ALLENIII,DAVIDA.COX,PETERLAXEditorsEmeriti:PETERHILTON,HARRYHOCHSTADT,JOHNTOLANDAcompletelistofthetitlesinthisseriesappearsattheen
2、dofthisvolume.FundamentalsofMatrixComputationsSecondEditionDAVIDS.WATKINSWILEY-INTERSCIENCEAJOHNWILEY&SONS,INC.,PUBLICATIONThistextisprintedonacid-freepaper.Copyright©2002byJohnWiley&Sons,Inc.,NewYork.Allrightsreserved.PublishedsimultaneouslyinCanada.Nopartofthispublicationmaybereproduced,
3、storedinaretrievalsystemortransmittedinanyformorbyanymeans,electronic,mechanical,photocopying,recording,scanningorotherwise,exceptaspermittedunderSection107or108ofthe1976UnitedStatesCopyrightAct,withouteitherthepriorwrittenpermissionofthePublisher,orauthorizationthroughpaymentoftheappropri
4、ateper-copyfeetotheCopyrightClearanceCenter,222RosewoodDrive,Danvers,MA01923,(978)750-8400,fax(978)750-4744.RequeststothePublisherforpermissionshouldbeaddressedtothePermissionsDepartment,JohnWiley&Sons,Inc.,605ThirdAvenue,NewYork,NY10158-0012,(212)850-6011,fax(212)850-6008,E-Mail:PERMREQ@W
5、ILEY.COM.Fororderingandcustomerservice,call1-800-CALLWILEY.LibraryofCongressCataloging-in-PublicationDataisavailable.ISBN0-471-21394-2PrintedintheUnitedStatesofAmerica1098765432ContentsPrefaceixAcknowledgmentsxiii1GaussianEliminationandItsVariants11.1MatrixMultiplication11.2SystemsofLinear
6、Equations111.3TriangularSystems231.4PositiveDefiniteSystems;CholeskyDecomposition321.5BandedPositiveDefiniteSystems541.6SparsePositiveDefiniteSystems631.7GaussianEliminationandtheLUDecomposition701.8GaussianEliminationwithPivoting931.9SparseGaussianElimination1062SensitivityofLinearSystems
7、1112.1VectorandMatrixNorms1122.2ConditionNumbers120viCONTENTS2.3PerturbingtheCoefficientMatrix1332.4APosterioriErrorAnalysisUsingtheResidual1372.5RoundoffErrors;BackwardStability1392.6PropagationofRoundoffErrors1482.7BackwardErrorAnalysisofGaussianElimination1
