数值分析
数值分析封面图

数值分析

(美) 萨奥尔 (Sauer,T.) , 著

出版社:机械工业出版社

年代:2012

定价:89.0

书籍简介:

本书是一本优秀的数值分析教材,全面论述了数值分析的基本方法,还介绍了诸如后向误差分析、稀疏矩阵计算及信号处理等内容。书中实例丰富,涉及计算机、电子、金融等各领域的应用,尤其是专门辟出“实例检验”部分,结合数值分析在各个学科中最新的应用,与Matlab软件紧密联系。

书籍目录:

PREFACE

CHAPTER0 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 Reading

CHAPTER 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 Wilki on polynomial

1.3.3 Se itivity 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 Method

Reality Check1:Kinematics ofthe Stewart platform

Software and Further Reading

CHAPTER 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 factorization

Reality 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 Spa e 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 Reading

CHAPTER 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 Curves

Reality Check3:Fonts from Bezier curves

SoftWare and Further Reading

CHAPTER 4Least Squares

4.1 Least Squares and the NormaI Equatio

4.1.1 Inco istent 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 Reading

CHAPTER 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 Quadrature

Reality Check5:Motion Control in Computer.Aided Modeling

SOftware and Further Reading

CHAPTER 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 Fi t.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 equatio

RealityCheck 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 Reading

CHAPTER 7 Boundary Value Problems

7.1 Shooting Method

7.1.1 Solutio of boundary value problems

7.1.2 Shooting Method implementation

Reality 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 Reading

CHAPTER 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 equatio

RealityCheck8: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 dime io

Software and Further Reading

CHAPTER 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 SDEs

Reality Check 9:The Black.Scholes FormulaSoftware and Further Reading

CHAPTER 10 Trigonometric Interpolation andthe FFT

10.1 The Fourier Tra foml

10.1.1 Complex arithmetic

10.1.2 Discrete FourierTra form

10.1.3 The Fast FourierTra form

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 Reading

CHAPTER 11 Compression

11.1 The Discrete Cosine Tra form

11.1.1 One.dime ionaI DCT

11.1.2 The DCT and least squares approximation

11.2 Two.Dime ionaI DCT and lmage Compression

11.2.1 Two.dime ional 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 CosineTra form

11.4.2 Bit quantization

Reality 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 lnve e 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 form

Reality 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 Dime ion reduction

12.4.3 Compression

12.4.4 Calculating the SVD

Software and Further Reading

CHAPTER 13 Optimization

13.1 Unco trained Optimization without Derivatives

13.1.1 Golden Section Search

13.1.2 Successive parabolic interpolation

13.1.3 Nelder.Mead search

13.2 Unco trained Optimization with Derivatives

13.2.1 Newton's Method

13.2.2 Steepest Descent

13.2.3 Conjugate Gradient Search

Reality 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

内容摘要:

《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。

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出版地北京出版单位机械工业出版社
版次1版印次1
定价(元)89.0语种英文
尺寸24 × 19装帧平装
页数 646 印数 3000

书籍信息归属:

数值分析是机械工业出版社于2012.6出版的中图分类号为 O241 的主题关于 数值分析-高等学校-教材-英文 的书籍。