数值分析 第二版（英文版）
出版时间：2012年版
内容简介
美国萨奥尔编著的《数值分析》是一本优秀的数值分析教材，书中不仅全面论述了数值分析的基本方法，还深入浅出地介绍了计算机和工程领域使用的一些高级数值方法，如压缩、前向和后向误差分析、求解方程组的迭代方法等。每章的“实例检验”部分结合数值分析在各领域的具体应用实例，进一步探究如何更好地应用数值分析方法解决实际问题。此外，书中含有一些算法的matlab实现代码，并且每章都配有大量难度适宜的习题和计算机问题，便于读者学习、巩固和提高。
目录
PREFACECHAPTER0 Fundamentals 0．1 Evaluating a Polynomial 0．2 Binary Numbe 0．2．1 Decimal to binary 0．2．2 Binary to decimaI 0．3 Floating Point Representation of ReaI Numbe 0．3．1 Floating point fclrmats 0．3．2 Machine reDresentatiOn 0．3．3 Addition offloating point numbe 0．4 Loss of Significance 0．5 Review of Calculus Software and Further ReadingCHAPTER 1 Solving Equatio 1．1 The Bisection Method 1．1．1 Bracketing a root 1．1．2 Howaccurate and howfast? 1．2 Fixed. Point Iteration 1．2．1 Fixed points of a function 1．2．2 Geometry of Fixed. Point lteration 1．2．3 Linear convergence of Fixed. Point Iteration 1．2．4 Stopping criteria 1．3 Limits of Accuracy 1．3．1 Forward and backward error 1．3．2 The Wilkion polynomial 1．3．3 Seitivity of root. finding 1．4 Newton's Method 1．4．1 Quadratic convergence of Newton's Method 1．4．2 Linear convergence of Newton's Method 1．5 Root. Finding without Derivatives 1．5．1 Secant Method and variants 1．5．2 Brent3 MethodReality Check1：Kinematics ofthe Stewart platform Software and Further ReadingCHAPTER 2 Systems of Equatio 2．1 Gaussian Elimination 2．1．1 Naive Gaussian elimination 2．1．2 Operation counts 2．2 The LU FactO rizatiOn 2．2．1 Matrix form of Gaussian elimination 2．2．2 Back substitution with the LU f2Ictorization 2．2．3 Complexity of the LU factorization 2．3 Sources of Error 2．3．1 Error magnification and condition number 2. 3．2 Swamping 2．4 The PA=LU FactOrization 2．4．1 PartiaI pivoting 2．4．2 Permutation matrices 2．4．3 PA=LU factorizationReality Check 2:The Euler. Bernoulli Beam 2．5 Iterative Methods 2．5．1 Jacobi Method 2．5．2 Gauss—Seidel Method and SOR 2．5．3 Convergence of iterative methods 2．5．4 Spae matrix computatio 2．6 Methods for symmetric positive. definite matrices 2．6．1 Symmetric positive. definite matrices 2．6．2 Cholesky factorization 2．6．3 Conjugate Gradient Method 2．6．4 PrecOnditioninq 2．7 Nonlinear Systems of Equatio 2．7．1 Multivariate Newton's Method 2．7．2 Broyden's Method Software and Further ReadingCHAPTER 3 Interpolation 3．1 Data and Interpolating Functio 3．1．1 Lagrange interpolation 3．1．2 Newton's divided differences 3．1．3 How many degree d polynomials pass through n points? 3．1．4 Code for interpolation 3．1．5 Representing functio by approximating polynomials 3．2 Interpolation Error 3．2．1 Interpolation error formula 3．2．2 Proof of Newton form and error formula 3．2．3 Runge phenomenon 3．3 Chebyshev Interpolation 3．3．1 Chebyshev's theorem 3．3．2 Chebyshev polynomials 3．3．3 Change of intervaI 3．4 Cubic Splines 3．4．1 Properties of splines 3．4．2 Endpoint conditio 3．5 BEzier CurvesReality Check3：Fonts from Bezier curves SoftWare and Further ReadingCHAPTER 4Least Squares 4．1 Least Squares and the NormaI Equatio 4．1．1 Incoistent systems of equatio 4．1．2 Fitting models to data 4．1．3 Conditioning of Ieast squares 4．2 A Survey of Models 4．2．1 Periodic data 4．2．2 Data linearization 4．3 QR Factorization 4．3．1 Gram. Schmidt OrthoaonaIizatiOn and Ieast squares 4．3．2 Modified Gram. Schmidt orthogonalization 4．3．3 Householder reflecto 4．4 Generalized Minimum ResiduaI(GMRES)Method 4．4．1 Krylov methods 4．4．2 PrecOnditiOned GMRES 4．5 Nonlinear Least Squares 4．5．1 Gauss. Newton Method 4．5．2 Models with nonlinear paramete 4．5．3 The Levenberg. Marquardt Method． Reatity Check4：GPS，Conditioning，and Nonlinear Least Squares Software and Further ReadingCHAPTER 5 NumericalDifferentiation and Inteqration 5．1 NumericaI Differentiation 5．1．1 Finite difference formulas 5．1．2 Rounding error 5．1．3 Extrapolation 5．1．4 Symbolic differentiation and integration 5．2 Newton. Cotes Formulas for NumericaI Integration 5．2．1 Trapezoid Rule 5．2．2 Simpson's Rule 5．2．3 Composite Newton. Cotes formulas 5．2．4 0pen Newton. Cotes Methods 5．3 Romberg Integration 5．4 Adaptive Quadrature 5．5 Gaussian QuadratureReality Check5：Motion Control in Computer. Aided Modeling SOftware and Further ReadingCHAPTER 6 Ordinary Differentiai Equatio 6．1 Initial Value Problems 6．1．1 Euler's Method 6．1．2 Existence,uniqueness．and continuity for solutio 6．1．3 Fit. order Iinear equatio 6．2 Analysis of IVP Solve 6．2．1 Local and global truncation error 6．2．2 The explicit Trapezoid Method 6．2．3 Taylor Methods 6．3 Systems of Ordinary Difl．erential Equatio 6．3．1 Higher 0rder equatio 6．3．2 Computer simulation：the pendulum 6．3．3 Computer simulation：orbitaI mechanics 6．4 Runge. Kutta Methods and Applicatio 6．4．1 The Runge. Kutta family 6．4．2 Computer simulation：the Hodgkin. Huxley neuron 6．4．3 Computer simulation：the Lorenz equatioRealityCheck 6The Tacoma Narrows Bridge 6．5 Variable Step. Size Methods 6．5．1 Embedded Runge. Kutta pai 6．5．2 0rder 4／5 methods 6．6 Implicit Methods and Sti仟Equatio 6．7 Multistep Methods 6．7．1 Generating multistep methods 6．7．2 Explicit multistep methods 6．7．3 Implicit multistep methods Software and Further ReadingCHAPTER 7 Boundary Value Problems 7．1 Shooting Method 7．1．1 Solutio of boundary value problems 7．1．2 Shooting Method implementationReality Check7:Buckling of a Circular Ring 7．2 Finite Difference Methods 7．2．1 Linear boundary value problems 7．2．2 Nonlinear boundary value problems 7．3 Collocation and the Finite Element Method 7．3．1 Collocation 7．3．2 Finite elements and the Galerkin Method Software and Further ReadingCHAPTER 8Partial Differential Equatio 8．1 Parabolic Equatio 8．1．1 Forward Difference Method 8．1．2 Stability analysis of Forward Difierence Method 8．1．3 Backward Di仟lerence Method 8．1．4 Crank. Nicolson Method 8．2 Hyperbolk：Equatio 8．2．1 The wave equation 8．2．2 The CFL condition 8．3 Elliptic Equatio 8．3．1 Finite Difference Method for elliptic equatioRealityCheck8：Heat distribution on a cooling fin 8．3．2 Finite Element Method for elliptic equatio 8．4 Nonlinear partial differential equatio 8．4．1 Implicit Newton solver 8．4．2 Nonlinear equatio in two space dimeio Software and Further ReadingCHAPTER 9 Random Numbe and Applicatio 9．1 Random Numbe 9．1．1 Pseudo. random numbe 9．1．2 Exponential and normal random numbe 9．2 Monte Carlo Simulation 9．2．1 Power Iaws for Monte Carlo estimation 9．2．2 Quasi. random numbe 9．3 Discrete and Continuous Brownian Motion 9．3．1 Random walks 9．3．2 Continuous Brownian motion 9．4 Stochastic DifFerential Equatio 9．4．1 Adding noise to differential equatio 9．4．2 NumericaI methods for SDEsReality Check 9：The Black. Scholes FormulaSoftware and FurtherReadingCHAPTER 10 Trigonometric Interpolation andthe FFT 10．1 The Fourier Trafoml 10．1．1 Complex arithmetic 10．1．2 Discrete FourierTraform 10．1．3 The Fast FourierTraform 10．2 Trigonometric Interpolation 10．2．1 The DFT Interpolation Theorem 10．2．2 E币cient evaluation of trigonometric functio 10．3 The FFT and Signal Processing 10．3．1 Orthogonality and interpolation 10．3．2 Least squares fitting with trigonometric functio 10．3．3 Sound，noise，and filtering Relity Check10：The Wiener Filter Software and Further ReadingCHAPTER 11 Compression 11．1 The Discrete Cosine Traform 11．1．1 One. dimeionaI DCT 11．1．2 The DCT and least squares approximation 11．2 Two. DimeionaI DCT and lmage Compression 11．2．1 Two. dimeional DCT 11．2．2 lmage compression 11．23 Quantization 11．3 HufFman Coding 11．3．1 Information theory and coding 11．3．2 Huffman coding for the JPEG format 11. 14 Modified DCT and Audio Compression 11．4．1 Modified Discrete CosineTraform 11．4．2 Bit quantizationReality Check11：A Simple Audio Codec Software and Further Reading CHAPTER12 Eigenvalues and Singular Values 12．I Power Iteration Methods 12．1．1 Power Iteration 12．1．2 Convergence of Power Iteration 12．1．3 lnvee Power Iteration 12．1．4 Rayleigh Quotient Iteration 12．2 QR Algorithm 12．2．1 Simultaneous iteration 12．2．2 ReaI Schur form and the QR algorithm 12．2．3 Upper Hessenberg formReality Check 12：How Sea~h Engines Rate Page Quality 12．3 Singular Value Decomposition 12．3．1 Finding the SVD in general 12．3．2 SpeciaI case：symmetric matrices 12．4 Applicatio of the SVD 12．4．1 Properties of the SVD 12．4．2 Dimeion reduction 12．4．3 Compression 12．4．4 Calculating the SVD Software and Further Reading CHAPTER 13 Optimization 13．1 Uncotrained Optimization without Derivatives 13．1．1 Golden Section Search 13．1．2 Successive parabolic interpolation 13．1．3 Nelder. Mead search 13．2 Uncotrained Optimization with Derivatives 13．2．1 Newton's Method 13．2．2 Steepest Descent 13．2．3 Conjugate Gradient SearchReality Check 13：Molecular Conformation and Numerical 0ptimization Software and Further Reading Appendix A A．1 Matrix Fundamentals A．2 Block Multiplication A．3 Eigenvalues and Eigenvecto A．4 Symmetric Matrices A．5 Vector Calculus Appendix B B．1 Starting MATLAB B．2 Graphics B．3 programming in MATLAB B．4 Flow Control B．5 Functio B．6 Matrix 0peratio B．7 Animation and Movies ANSWERS T0 SELECTED EXERCISES BIBLIOGRAPHY INDEX
