数值分析

图书标准信息

• 作者 [美]Timothy Sauer 著
• 出版社 机械工业出版社
• 出版时间 2012-06
• 版次 2
• ISBN 9787111385820
• 定价 89.00元
• 装帧 平装
• 开本 16开
• 纸张 胶版纸
• 页数 646页
• 正文语种 英语
• 原版书名 Numerical Analysis, Second Edition
• 丛书 华章数学原版精品系列

【内容简介】

　　《数值分析（英文版·第2版）》英文影印版由Pearson Education Asia Ltd.授权机械工业出版社独家出版。未经出版者书面许可，不得以任何方式复制或抄袭本书内容。

【作者简介】

Timothy Sauer 乔治梅森大学数学系教授。1982年于加州大学伯克利分校获得数学专业博士学位，师从著名数学家Robin Hartshorne。他的主要研究领域为动力系统、计算数学和数学生物学。他是《SIAM Journal on Applied Dynamical Systems》、《Journal of Difference Equations and Applications》和《Physica D》等学术期刊的编委。

【目录】

PREFACE
CHAPTER0Fundamentals
0.1EvaluatingaPolynomial
0.2BinaryNumbe 
0.2.1Decimaltobinary
0.2.2BinarytodecimaI
0.3FloatingPointRepresentationofReaINumbe 
0.3.1Floatingpointfclrmats
0.3.2MachinereDresentatiOn
0.3.3Additionoffloatingpointnumbe 
0.4LossofSignificance
0.5ReviewofCalculus
SoftwareandFurtherReading
CHAPTER1SolvingEquatio 
1.1TheBisectionMethod
1.1.1Bracketingaroot
1.1.2Howaccurateandhowfast？
1.2Fixed.PointIteration
1.2.1Fixedpointsofafunction
1.2.2GeometryofFixed.Pointlteration
1.2.3LinearconvergenceofFixed.PointIteration
1.2.4Stoppingcriteria
1.3LimitsofAccuracy
1.3.1Forwardandbackwarderror
1.3.2TheWilki onpolynomial
1.3.3Se itivityofroot.finding
1.4Newton'sMethod
1.4.1QuadraticconvergenceofNewton'sMethod
1.4.2LinearconvergenceofNewton'sMethod
1.5Root.FindingwithoutDerivatives
1.5.1SecantMethodandvariants
1.5.2Brent3Method
RealityCheck1：KinematicsoftheStewartplatform
SoftwareandFurtherReading
CHAPTER2SystemsofEquatio 
2.1GaussianElimination
2.1.1NaiveGaussianelimination
2.1.2Operationcounts
2.2TheLUFactOrizatiOn
2.2.1MatrixformofGaussianelimination
2.2.2BacksubstitutionwiththeLUf2Ictorization
2.2.3ComplexityoftheLUfactorization
2.3SourcesofError
2.3.1Errormagnificationandconditionnumber
2.3.2Swamping
2.4ThePA=LUFactOrization
2.4.1PartiaIpivoting
2.4.2Permutationmatrices
2.4.3PA=LUfactorization
RealityCheck2:TheEuler.BernoulliBeam
2.5IterativeMethods
2.5.1JacobiMethod
2.5.2Gauss—SeidelMethodandSOR
2.5.3Convergenceofiterativemethods
2.5.4Spa ematrixcomputatio 
2.6Methodsforsymmetricpositive.definitematrices
2.6.1Symmetricpositive.definitematrices
2.6.2Choleskyfactorization
2.6.3ConjugateGradientMethod
2.6.4PrecOnditioninq
2.7NonlinearSystemsofEquatio 
2.7.1MultivariateNewton'sMethod
2.7.2Broyden'sMethod
SoftwareandFurtherReading
CHAPTER3Interpolation
3.1DataandInterpolatingFunctio 
3.1.1Lagrangeinterpolation
3.1.2Newton'sdivideddifferences
3.1.3Howmanydegreedpolynomialspassthroughn
points？
3.1.4Codeforinterpolation
3.1.5Representingfunctio byapproximatingpolynomials
3.2InterpolationError
3.2.1Interpolationerrorformula
3.2.2ProofofNewtonformanderrorformula
3.2.3Rungephenomenon
3.3ChebyshevInterpolation
3.3.1Chebyshev'stheorem
3.3.2Chebyshevpolynomials
3.3.3ChangeofintervaI
3.4CubicSplines
3.4.1Propertiesofsplines
3.4.2Endpointconditio 
3.5BEzierCurves
RealityCheck3：FontsfromBeziercurves
SoftWareandFurtherReading
CHAPTER4LeastSquares
4.1LeastSquaresandtheNormaIEquatio 
4.1.1Inco istentsystemsofequatio 
4.1.2Fittingmodelstodata
4.1.3ConditioningofIeastsquares
4.2ASurveyofModels
4.2.1Periodicdata
4.2.2Datalinearization
4.3QRFactorization
4.3.1Gram.SchmidtOrthoaonaIizatiOnandIeastsquares
4.3.2ModifiedGram.Schmidtorthogonalization
4.3.3Householderreflecto 
4.4GeneralizedMinimumResiduaI（GMRES）Method
4.4.1Krylovmethods
4.4.2PrecOnditiOnedGMRES
4.5NonlinearLeastSquares
4.5.1Gauss.NewtonMethod
4.5.2Modelswithnonlinearparamete 
4.5.3TheLevenberg.MarquardtMethod.
ReatityCheck4：GPS，Conditioning，andNonlinearLeastSquares
SoftwareandFurtherReading
CHAPTER5NumericalDifferentiationand
Inteqration
5.1NumericaIDifferentiation
5.1.1Finitedifferenceformulas
5.1.2Roundingerror
5.1.3Extrapolation
5.1.4Symbolicdifferentiationandintegration
5.2Newton.CotesFormulasforNumericaIIntegration
5.2.1TrapezoidRule
5.2.2Simpson'sRule
5.2.3CompositeNewton.Cotesformulas
5.2.40penNewton.CotesMethods
5.3RombergIntegration
5.4AdaptiveQuadrature
5.5GaussianQuadrature
RealityCheck5：MotionControlinComputer.AidedModeling
SOftwareandFurtherReading
CHAPTER6OrdinaryDifferentiaiEquatio 
6.1InitialValueProblems
6.1.1Euler'sMethod
6.1.2Existence,uniqueness.andcontinuityforsolutio 
6.1.3Fi t.orderIinearequatio 
6.2AnalysisofIVPSolve 
6.2.1Localandglobaltruncationerror
6.2.2TheexplicitTrapezoidMethod
6.2.3TaylorMethods
6.3SystemsofOrdinaryDifl.erentialEquatio 
6.3.1Higher0rderequatio 
6.3.2Computersimulation：thependulum
6.3.3Computersimulation：orbitaImechanics
6.4Runge.KuttaMethodsandApplicatio 
6.4.1TheRunge.Kuttafamily
6.4.2Computersimulation：theHodgkin.Huxleyneuron
6.4.3Computersimulation：theLorenzequatio 
RealityCheck6TheTacomaNarrowsBridge
6.5VariableStep.SizeMethods
6.5.1EmbeddedRunge.Kuttapai 
6.5.20rder4／5methods
6.6ImplicitMethodsandSti仟Equatio 
6.7MultistepMethods
6.7.1Generatingmultistepmethods
6.7.2Explicitmultistepmethods
6.7.3Implicitmultistepmethods
SoftwareandFurtherReading
CHAPTER7BoundaryValueProblems
7.1ShootingMethod
7.1.1Solutio ofboundaryvalueproblems
7.1.2ShootingMethodimplementation
RealityCheck7:BucklingofaCircularRing
7.2FiniteDifferenceMethods
7.2.1Linearboundaryvalueproblems
7.2.2Nonlinearboundaryvalueproblems
7.3CollocationandtheFiniteElementMethod
7.3.1Collocation
7.3.2FiniteelementsandtheGalerkinMethod
SoftwareandFurtherReading
CHAPTER8PartialDifferentialEquatio 
8.1ParabolicEquatio 
8.1.1ForwardDifferenceMethod
8.1.2StabilityanalysisofForwardDifierenceMethod
8.1.3BackwardDi仟lerenceMethod
8.1.4Crank.NicolsonMethod
8.2Hyperbolk：Equatio 
8.2.1Thewaveequation
8.2.2TheCFLcondition
8.3EllipticEquatio 
8.3.1FiniteDifferenceMethodforellipticequatio 
RealityCheck8：Heatdistributiononacoolingfin
8.3.2FiniteElementMethodforellipticequatio 
8.4Nonlinearpartialdifferentialequatio 
8.4.1ImplicitNewtonsolver
8.4.2Nonlinearequatio intwospacedime io 
SoftwareandFurtherReading
CHAPTER9RandomNumbe andApplicatio 
9.1RandomNumbe 
9.1.1Pseudo.randomnumbe 
9.1.2Exponentialandnormalrandomnumbe 
9.2MonteCarloSimulation
9.2.1PowerIawsforMonteCarloestimation
9.2.2Quasi.randomnumbe 
9.3DiscreteandContinuousBrownianMotion
9.3.1Randomwalks
9.3.2ContinuousBrownianmotion
9.4StochasticDifFerentialEquatio 
9.4.1Addingnoisetodifferentialequatio 
9.4.2NumericaImethodsforSDEs
RealityCheck9：TheBlack.ScholesFormulaSoftwareandFurtherReading
CHAPTER10TrigonometricInterpolationandtheFFT
10.1TheFourierTra foml
10.1.1Complexarithmetic
10.1.2DiscreteFourierTra form
10.1.3TheFastFourierTra form
10.2TrigonometricInterpolation
10.2.1TheDFTInterpolationTheorem
10.2.2E币cientevaluationoftrigonometricfunctio 
10.3TheFFTandSignalProcessing
10.3.1Orthogonalityandinterpolation
10.3.2Leastsquaresfittingwithtrigonometricfunctio 
10.3.3Sound，noise，andfiltering
RelityCheck10：TheWienerFilter
SoftwareandFurtherReading
CHAPTER11Compression
11.1TheDiscreteCosineTra form
11.1.1One.dime ionaIDCT
11.1.2TheDCTandleastsquaresapproximation
11.2Two.Dime ionaIDCTandlmageCompression
11.2.1Two.dime ionalDCT
11.2.2lmagecompression
11.23Quantization
11.3HufFmanCoding
11.3.1Informationtheoryandcoding
11.3.2HuffmancodingfortheJPEGformat
11.14ModifiedDCTandAudioCompression
11.4.1ModifiedDiscreteCosineTra form
11.4.2Bitquantization
RealityCheck11：ASimpleAudioCodec
SoftwareandFurtherReading
CHAPTER12EigenvaluesandSingularValues
12.IPowerIterationMethods
12.1.1PowerIteration
12.1.2ConvergenceofPowerIteration
12.1.3lnve ePowerIteration
12.1.4RayleighQuotientIteration
12.2QRAlgorithm
12.2.1Simultaneousiteration
12.2.2ReaISchurformandtheQRalgorithm
12.2.3UpperHessenbergform
RealityCheck12：HowSea~hEnginesRatePageQuality
12.3SingularValueDecomposition
12.3.1FindingtheSVDingeneral
12.3.2SpeciaIcase：symmetricmatrices
12.4Applicatio oftheSVD
12.4.1PropertiesoftheSVD
12.4.2Dime ionreduction
12.4.3Compression
12.4.4CalculatingtheSVD
SoftwareandFurtherReading
CHAPTER13Optimization
13.1Unco trainedOptimizationwithoutDerivatives
13.1.1GoldenSectionSearch
13.1.2Successiveparabolicinterpolation
13.1.3Nelder.Meadsearch
13.2Unco trainedOptimizationwithDerivatives
13.2.1Newton'sMethod
13.2.2SteepestDescent
13.2.3ConjugateGradientSearch
RealityCheck13：MolecularConformationandNumerical
0ptimization
SoftwareandFurtherReading
AppendixA
A.1MatrixFundamentals
A.2BlockMultiplication
A.3EigenvaluesandEigenvecto 
A.4SymmetricMatrices
A.5VectorCalculus
AppendixB
B.1StartingMATLAB
B.2Graphics
B.3programminginMATLAB
B.4FlowControl
B.5Functio 
B.6Matrix0peratio 
B.7AnimationandMovies
ANSWERST0SELECTEDEXERCISES
BIBLIOGRAPHY
INDEX