数值分析PDF|Epub|txt|kindle电子书版本网盘下载

数值分析PDF格式电子书版下载

注意：本站所有压缩包均有解压码： 点击下载压缩包解压工具

1 Mathematical Preliminaries1

1.1 Review of Calculus2

1.2 Roundoff Errors and Computer Arithmetic18

1.3 Algorithms and Convergence31

1.4 Numerical Software40

2 Solutions of Equations in One Variable47

2.1 The Bisection Method48

2.2 Fixed-Point Iteration55

2.3 Newton’s Method66

2.4 Error Analysis for Iterative Methods78

2.5 Accelerating Convergence86

2.6 Zeros of Polynomials and Müller’s Method91

2.7 Survey of Methods and Software101

3 Interpolation and Polynomial Approximation104

3.1 Interpolation and the Lagrange Polynomial107

3.2 Divided Differences122

3.3 Hermite Interpolation133

3.4 Cubic Spline Interpolation141

3.5 Parametric Curves156

3.6 Survey of Methods and Software163

4 Numerical Differentiation and Integration166

4.1 Numerical Differentiation167

4.2 Richardson’s Extrapolation178

4.3 Elements of Numerical Integration186

4.4 Composite Numerical Integration196

4.5 Romberg Integration207

4.6 Adaptive Quadrature Methods213

4.7 Gaussian Quadrature220

4.8 Multiple Integrals227

4.9 Improper Integrals241

4.10 Survey of Methods and Software247

5 Initial-Value Problems for Ordinary Differential Equations249

5.1 The Elementary Theory of Initial-Value Problems251

5.2 Euler’s Method256

5.3 Higher-Order Taylor Methods266

5.4 Runge-Kutta Methods272

5.5 Error Control and the Runge-Kutta-Fehlberg Method282

5.6 Multistep Methods289

5.7 Variable Step-Size Multistep Methods301

5.8 Extrapolation Methods307

5.9 Higher-Order Equations and Systems of Differential Equations313

5.10 Stability324

5.11 Stiff Differential Equations334

5.12 Survey of Methods and Software342

6 Direct Methods for Solving Linear Systems344

6.1 Linear Systems of Equations345

6.2 Pivoting Strategies359

6.3 Linear Algebra and Matrix Inversion370

6.4 The Daterminant of a Matrix383

6.5 Matrix Factorization388

6.6 Special Types of Matrices398

6.7 Survey of Methods and Software413

7 Iterative Techniques in Matrix Algebra417

7.1 Norms of Vectors and Matrices418

7.2 Eigenvalues and Eigenvectors430

7.3 Iterative Techniques for Solving Linear Systems437

7.4 Error Bounds and Iterative Refinement454

7.5 The Conjugate Gradient Method465

7.6 Survey of Methods and Software481

8 Approximation Theory483

8.1 Discrete Least Squares Approximation484

8.2 Orthogonal Polynomials and Least Squares Approximation498

8.3 Chebyshev Polynomials and Economization of Power Series507

8.4 Rational Function Approximation517

8.5 Trigonometric Polynomial Approximation529

8.6 Fast Fourier Transforms537

8.7 Survey of Methods and Software548

9 Approximating Eigenvalues550

9.1 Linear Algebra and Eigenvalues551

9.2 The Power Method560

9.3 Householder’s Method577

9.4 The QR Algorithm585

9.5 Survey of Methods and Software597

10 Numerical Solutions of Nonlinear Systems of Equations600

10.1 Fixed Points for Functions of Several Variables602

10.2 Newton’s Method611

10.3 Quasi-Newton Methods620

10.4 Steepest Descent Techniques628

10.5 Homotopy and Continuation Methods635

10.6 Survey of Methods and Software643

11 Boundary-Value Problems for Ordinary Differential Equations645

11.1 The Linear Shooting Method646

11.2 The Shooting Method for Nonlinear Prblems653

11.3 Finite-Difference Methods for Linear Problems660

11.4 Finite-Difference Methods for Nonlinear Problems667

11.5 The Rayleigh-Ritz Method672

11.6 Survey of Methods and Software688

12 Numerical Solutions to Partial Differential Equations691

12.1 Elliptic Partial Differential Equations694

12.2 Parabolic Partial Differential Equations704

12.3 Hyperbolic Partial Differential Equations718

12.4 An Introduction to the Finite-Element Method726

12.5 Survey of Methods and Software741

Bibliography743

Answers to Selected Exercises753

Index831