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NUMERICAL COMPUTING WITH MATLAB【2025|PDF下载-Epub版本|mobi电子书|kindle百度云盘下载】

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出版社： SIAM PRESS
ISBN：0898715601
出版时间：2004
标注页数：336页
文件大小：57MB
文件页数：347页
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图书目录

1 Introduction to MATLAB1

1.1 The Golden Ratio1

1.2 Fibonacci Numbers7

1.3 Fractal Fern13

1.4 Magic Squares18

1.5 Cryptography26

1.6 The 3n+1 Sequence31

1.7 Floating-Point Arithmetic33

1.8 Further Reading41

Exercises41

2 Linear Equations53

2.1 Solving Linear Systems53

2.2 The MATLAB Backslash Operator54

2.3 A 3-by-3 Example54

2.4 Permutation and Triangular Matrices56

2.5 LU Factorization57

2.6 Why Is Pivoting Necessary？58

2.7 lutx，bslashtx，lugui60

2.8 Effect of Roundoff Errors63

2.9 Norms and Condition Numbers66

2.10 Sparse Matrices and Band Matrices72

2.11 PageRank and Markov Chains74

2.12 Further Reading81

Exercises82

3 Interpolation93

3.1 The Interpolating Polynomial93

3.2 Piecewise Linear Interpolation98

3.3 Piecewise Cubic Hermite Interpolation99

3.4 Shape-Preserving Piecewise Cubic100

3.5 Cubic Spline102

3.6 pchiptx，splinetx105

3.7 interpgui108

Exercises110

4 Zeros and Roots117

4.1 Bisection117

4.2 Newton’s Method119

4.3 A Perverse Example121

4.4 Secant Method122

4.5 Inverse Quadratic Interpolation123

4.6 Zeroin124

4.7 fzerotx，feval124

4.8 fzerogui129

4.9 Value Finding and Reverse Interpolation132

4.10 Optimization and fmintx132

Exercises135

5 Least Squares141

5.1 Models and Curve Fitting141

5.2 Norms143

5.3 censusgui144

5.4 Householder Reflections145

5.5 The QR Factorization147

5.6 Pseudoinverse152

5.7 Rank Deficiency154

5.8 Separable Least Squares156

5.9 Further Reading159

Exercises159

6 Quadrature167

6.1 Adaptive Quadrature167

6.2 Basic Quadrature Rules168

6.3 quadtx，quadgui170

6.4 Specifying Integrands173

6.5 Performance175

6.6 Integrating Discrete Data177

6.7 Further Reading179

Exercises179

7 Ordinary Differential Equations187

7.1 Integrating Differential Equations187

7.2 Systems of Equations188

7.3 Linearized Differential Equations189

7.4 Single-Step Methods191

7.5 The BS23 Algorithm194

7.6 ode23tx196

7.7 Examples199

7.8 Lorenz Attractor202

7.9 Stiffness204

7.10 Events208

7.11 Multistep Methods212

7.12 The MATLAB ODE Solvers212

7.13 Errors213

7.14 Performance217

7.15 Further Reading219

Exercises219

8 Fourier Analysis237

8.1 Touch-Tone Dialing237

8.2 Finite Fourier Transform241

8.3 fftgui242

8.4 Sunspots244

8.5 Periodic Time Series248

8.6 Fast Finite Fourier Transform249

8.7 ffttx250

8.8 fftmatrix251

8.9 Other Fourier Transforms and Series252

8.10 Further Reading254

Exercises254

9 Random Numbers257

9.1 Pseudorandom Numbers257

9.2 Uniform Distribution257

9.3 Normal Distribution260

9.4 randtx，randntx263

Exercises265

10 Eigenvalues and Singular Values269

10.1 Eigenvalue and Singular Value Decompositions269

10.2 A Small Example272

10.3 eigshow273

10.4 Characteristic Polynomial275

10.5 Symmetric and Hermitian Matrices276

10.6 Eigenvalue Sensitivity and Accuracy277

10.7 Singular Value Sensitivity and Accuracy283

10.8 Jordan and Schur Forms284

10.9 The QR Algorithm285

10.10 eigsvdgui287

10.11 Principal Components289

10.12 Circle Generator293

10.13 Further Reading298

Exercises298

11 Partial Differential Equations307

11.1 Model Problems307

11.2 Finite Difference Methods308

11.3 Matrix Representation310

11.4 Numerical Stability312

11.5 The L-Shaped Membrane314

Exercises319

Bibliography327

Index332