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1、AnIntroductiontoNumericalAnalysisEndreS¨uliandDavidF.MayersUniversityofOxfordpublishedbythepresssyndicateoftheuniversityofcambridgeThePittBuilding,TrumpingtonStreet,Cambridge,UnitedKingdomcambridgeuniversitypressTheEdinburghBuilding,CambridgeCB22RU,UK40West20thStreet,NewYork,NY100
2、11-4211,USA477WilliamstownRoad,PortMelbourne,VIC3207,AustraliaRuizdeAlarc´on13,28014Madrid,SpainDockHouse,TheWaterfront,CapeTown8001,SouthAfricahttp://www.cambridge.orgCCambridgeUniversityPress,2003Thisbookisincopyright.Subjecttostatutoryexceptionandtotheprovisionsofrelevantcolle
3、ctivelicensingagreements,noreproductionofanypartmaytakeplacewithoutthewrittenpermissionofCambridgeUniversityPress.Firstpublished2003PrintedintheUnitedKingdomattheUniversityPress,CambridgeTypefaceCMR10/13ptSystemLATEX2ε[TB]AcataloguerecordforthisbookisavailablefromtheBritishLibrary
4、LibraryofCongressCataloguinginPublicationdataISBN0521810264hardbackISBN0521007941paperbackContentsPrefacepagevii1Solutionofequationsbyiteration11.1Introduction11.2Simpleiteration21.3Iterativesolutionofequations171.4RelaxationandNewton’smethod191.5Thesecantmethod251.6Thebisectionme
5、thod281.7Globalbehaviour291.8Notes32Exercises352Solutionofsystemsoflinearequations392.1Introduction392.2Gaussianelimination442.3LUfactorisation482.4Pivoting522.5Solutionofsystemsofequations552.6Computationalwork562.7Normsandconditionnumbers582.8Hilbertmatrix722.9Leastsquaresmethod
6、742.10Notes79Exercises823Specialmatrices873.1Introduction873.2Symmetricpositivedefinitematrices873.3Tridiagonalandbandmatrices93iiiivContents3.4Monotonematrices983.5Notes101Exercises1024Simultaneousnonlinearequations1044.1Introduction1044.2Simultaneousiteration1064.3RelaxationandNe
7、wton’smethod1164.4Globalconvergence1234.5Notes124Exercises1265Eigenvaluesandeigenvectorsofasymmetricmatrix1335.1Introduction1335.2Thecharacteristicpolynomial1375.3Jacobi’smethod1375.4TheGerschgorintheorems1455.5Householder’smethod1505.6Eigenvaluesofatridiagonalmatrix1565.7TheQRalg
8、orithm1625.7.1TheQRfactorisationr
