18ddf2ba0092217b59726b053d7a4155 (2).pdf

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THEARTOFSCIENTIFICCOMPUTING（ISBN0-521-43108-5）Copyright（C）1988-1992byCambridgeUniversityPress.ProgramsCopyright（C）1988-1992byNumericalRecipesSoftware.Permissionisgrantedforinternetuserstomakeonepapercopyfortheirownpersonaluse.Furtherreproduction,oranycopyingofmachine-readablefiles（includingthisone）toanyservercomputer,isstrictlyprohibited.ToorderNumericalRecipesbooksorCDROMs,visitwebsitehttp:

/orcall1-800-872-7423（NorthAmericaonly）,orsendemailtodirectcustservcambridge.org（outsideNorthAmerica）.NumericalRecipesinCTheArtofScientificComputingSecondEditionWilliamH.PressHarvard-SmithsonianCenterforAstrophysicsSaulA.TeukolskyDepartmentofPhysics,CornellUniversityWilliamT.VetterlingPolaroidCorporationBrianP.FlanneryEXXONResearchandEngineeringCompanyCAMBRIDGEUNIVERSITYPRESSCambridgeNewYorkPortChesterMelbourneSydneySamplepagefromNUMERICALRECIPESINC:

THEARTOFSCIENTIFICCOMPUTING（ISBN0-521-43108-5）Copyright（C）1988-1992byCambridgeUniversityPress.ProgramsCopyright（C）1988-1992byNumericalRecipesSoftware.Permissionisgrantedforinternetuserstomakeonepapercopyfortheirownpersonaluse.Furtherreproduction,oranycopyingofmachine-readablefiles（includingthisone）toanyservercomputer,isstrictlyprohibited.ToorderNumericalRecipesbooksorCDROMs,visitwebsitehttp:

/orcall1-800-872-7423（NorthAmericaonly）,orsendemailtodirectcustservcambridge.org（outsideNorthAmerica）.PublishedbythePressSyndicateoftheUniversityofCambridgeThePittBuilding,TrumpingtonStreet,CambridgeCB21RP40West20thStreet,NewYork,NY10011-4211,USA477WilliamstownRoad,PortMelbourne,VIC,3207,AustraliaCopyrightc?

CambridgeUniversityPress1988,1992exceptfor13.10andAppendixB,whichareplacedintothepublicdomain,andexceptforallothercomputerprogramsandprocedures,whichareCopyrightc?

NumericalRecipesSoftware1987,1988,1992,1997,2002AllRightsReserved.Somesectionsofthisbookwereoriginallypublished,indifferentform,inComputersinPhysicsmagazine,Copyrightc?

AmericanInstituteofPhysics,19881992.FirstEditionoriginallypublished1988;SecondEditionoriginallypublished1992.Reprintedwithcorrections,1993,1994,1995,1997,2002.Thisreprintingiscorrectedtosoftwareversion2.10PrintedintheUnitedStatesofAmericaTypesetinTEXWithoutanadditionallicensetousethecontainedsoftware,thisbookisintendedasatextandreferencebook,forreadingpurposesonly.Afreelicenseforlimiteduseofthesoftwarebytheindividualownerofacopyofthisbookwhopersonallytypesoneormoreroutinesintoasinglecomputerisgrantedundertermsdescribedonp.xvii.Seethesection“LicenseInformation”（pp.xvixviii）forinformationonobtainingmoregenerallicensesatlowcost.Machine-readablemediacontainingthesoftwareinthisbook,withincludedlicensesforuseonasinglescreen,areavailablefromCambridgeUniversityPress.Seetheorderformatthebackofthebook,emailto“orderscup.org”（NorthAmerica）or“directcustservcambridge.org”（restofworld）,orwritetoCambridgeUniversityPress,110MidlandAvenue,PortChester,NY10573（USA）,forfurtherinformation.Thesoftwaremayalsobedownloaded,withimmediatepurchaseofalicensealsopossible,fromtheNumericalRecipesSoftwareWebSite（http:

/）.UnlicensedtransferofNumericalRecipesprogramstoanyotherformat,ortoanycomputerexceptonethatisspecificallylicensed,isstrictlyprohibited.Technicalquestions,corrections,andrequestsforinformationshouldbeaddressedtoNumericalRecipesSoftware,P.O.Box380243,Cambridge,MA02238-0243（USA）,email“”,orfax781863-1739.LibraryofCongressCataloginginPublicationDataNumericalrecipesinC:

theartofscientificcomputing/WilliamH.Press.etal.2nded.Includesbibliographicalreferences（p.）andindex.ISBN0-521-43108-51.NumericalanalysisComputerprograms.2.ScienceMathematicsComputerprograms.3.C（Computerprogramlanguage）I.Press,WilliamH.QA297.N8661992519.4?

0285?

53dc2092-8876AcatalogrecordforthisbookisavailablefromtheBritishLibrary.ISBN0521431085BookISBN0521437202ExamplebookinCISBN0521750377C/C+CDROM（Windows/Macintosh）ISBN0521750350CompleteCDROM（Windows/Macintosh）ISBN0521750369CompleteCDROM（UNIX/Linux）SamplepagefromNUMERICALRECIPESINC:

THEARTOFSCIENTIFICCOMPUTING（ISBN0-521-43108-5）Copyright（C）1988-1992byCambridgeUniversityPress.ProgramsCopyright（C）1988-1992byNumericalRecipesSoftware.Permissionisgrantedforinternetuserstomakeonepapercopyfortheirownpersonaluse.Furtherreproduction,oranycopyingofmachine-readablefiles（includingthisone）toanyservercomputer,isstrictlyprohibited.ToorderNumericalRecipesbooksorCDROMs,visitwebsitehttp:

/orcall1-800-872-7423（NorthAmericaonly）,orsendemailtodirectcustservcambridge.org（outsideNorthAmerica）.ContentsPrefacetotheSecondEditionxiPrefacetotheFirstEditionxivLicenseInformationxviComputerProgramsbyChapterandSectionxix1Preliminaries11.0Introduction11.1ProgramOrganizationandControlStructures51.2SomeCConventionsforScientificComputing151.3Error,Accuracy,andStability282SolutionofLinearAlgebraicEquations322.0Introduction322.1Gauss-JordanElimination362.2GaussianEliminationwithBacksubstitution412.3LUDecompositionandItsApplications432.4TridiagonalandBandDiagonalSystemsofEquations502.5IterativeImprovementofaSolutiontoLinearEquations552.6SingularValueDecomposition592.7SparseLinearSystems712.8VandermondeMatricesandToeplitzMatrices902.9CholeskyDecomposition962.10QRDecomposition982.11IsMatrixInversionanN3Process?

1023InterpolationandExtrapolation1053.0Introduction1053.1PolynomialInterpolationandExtrapolation1083.2RationalFunctionInterpolationandExtrapolation1113.3CubicSplineInterpolation1133.4HowtoSearchanOrderedTable1173.5CoefficientsoftheInterpolatingPolynomial1203.6InterpolationinTwoorMoreDimensions123vviContentsSamplepagefromNUMERICALRECIPESINC:

THEARTOFSCIENTIFICCOMPUTING（ISBN0-521-43108-5）Copyright（C）1988-1992byCambridgeUniversityPress.ProgramsCopyright（C）1988-1992byNumericalRecipesSoftware.Permissionisgrantedforinternetuserstomakeonepapercopyfortheirownpersonaluse.Furtherreproduction,oranycopyingofmachine-readablefiles（includingthisone）toanyservercomputer,isstrictlyprohibited.ToorderNumericalRecipesbooksorCDROMs,visitwebsitehttp:

/orcall1-800-872-7423（NorthAmericaonly）,orsendemailtodirectcustservcambridge.org（outsideNorthAmerica）.4IntegrationofFunctions1294.0Introduction1294.1ClassicalFormulasforEquallySpacedAbscissas1304.2ElementaryAlgorithms1364.3RombergIntegration1404.4ImproperIntegrals1414.5GaussianQuadraturesandOrthogonalPolynomials1474.6MultidimensionalIntegrals1615EvaluationofFunctions1655.0Introduction1655.1SeriesandTheirConvergence1655.2EvaluationofContinuedFractions1695.3PolynomialsandRationalFunctions1735.4ComplexArithmetic1765.5RecurrenceRelationsandClenshawsRecurrenceFormula1785.6QuadraticandCubicEquations1835.7NumericalDerivatives1865.8ChebyshevApproximation1905.9DerivativesorIntegralsofaChebyshev-approximatedFunction1955.10PolynomialApproximationfromChebyshevCoefficients1975.11EconomizationofPowerSeries1985.12PadeApproximants2005.13RationalChebyshevApproximation2045.14EvaluationofFunctionsbyPathIntegration2086SpecialFunctions2126.0Introduction2126.1GammaFunction,BetaFunction,Factorials,BinomialCoefficients2136.2IncompleteGammaFunction,ErrorFunction,Chi-SquareProbabilityFunction,CumulativePoissonFunction2166.3ExponentialIntegrals2226.4IncompleteBetaFunction,StudentsDistribution,F-Distribution,CumulativeBinomialDistribution2266.5BesselFunctionsofIntegerOrder2306.6ModifiedBesselFunctionsofIntegerOrder2366.7BesselFunctionsofFractionalOrder,AiryFunctions,SphericalBesselFunctions2406.8SphericalHarmonics2526.9FresnelIntegrals,CosineandSineIntegrals2556.10DawsonsIntegral2596.11EllipticIntegralsandJacobianEllipticFunctions2616.12HypergeometricFunctions2717RandomNumbers2747.0Introduction2747.1UniformDeviates275ContentsviiSamplepagefromNUMERICALRECIPESINC:

THEARTOFSCIENTIFICCOMPUTING（ISBN0-521-43108-5）Copyright（C）1988-1992byCambridgeUniversityPress.ProgramsCopyright（C）1988-1992byNumericalRecipesSoftware.Permissionisgrantedforinternetuserstomakeonepapercopyfortheirownpersonaluse.Furtherreproduction,oranycopyingofmachine-readablefiles（includingthisone）toanyservercomputer,isstrictlyprohibited.ToorderNumericalRecipesbooksorCDROMs,visitwebsitehttp:

/orcall1-800-872-7423（NorthAmericaonly）,orsendemailtodirectcustservcambridge.org（outsideNorthAmerica）.7.2TransformationMethod:

ExponentialandNormalDeviates2877.3RejectionMethod:

Gamma,Poisson,BinomialDeviates2907.4GenerationofRandomBits2967.5RandomSequencesBasedonDataEncryption3007.6SimpleMonteCarloIntegration3047.7Quasi-（thatis,Sub-）RandomSequences3097.8AdaptiveandRecursiveMonteCarloMethods3168Sorting3298.0Introduction3298.1StraightInsertionandShellsMethod3308.2Quicksort3328.3Heapsort3368.4IndexingandRanking3388.5SelectingtheMthLargest3418.6DeterminationofEquivalenceClasses3459RootFindingandNonlinearSetsofEquations3479.0Introduction3479.1BracketingandBisection3509.2SecantMethod,FalsePositionMethod,andRiddersMethod3549.3VanWijngaardenDekkerBrentMethod3599.4Newton-RaphsonMethodUsingDerivative3629.5RootsofPolynomials3699.6Newton-RaphsonMethodforNonlinearSystemsofEquations3799.7GloballyConvergentMethodsforNonlinearSystemsofEquations38310MinimizationorMaximizationofFunctions39410.0Introduction39410.1GoldenSectionSearchinOneDimension39710.2ParabolicInt