NUMERICAL COMPUTING WITH MATLABpdf电子书版本下载

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1 Introduction to MATLAB 1

1.1 The Golden Ratio 1

1.2 Fibonacci Numbers 7

1.3 Fractal Fern 13

1.4 Magic Squares 18

1.5 Cryptography 26

1.6 The 3n+1 Sequence 31

1.7 Floating-Point Arithmetic 33

1.8 Further Reading 41

Exercises 41

2 Linear Equations 53

2.1 Solving Linear Systems 53

2.2 The MATLAB Backslash Operator 54

2.3 A 3-by-3 Example 54

2.4 Permutation and Triangular Matrices 56

2.5 LU Factorization 57

2.6 Why Is Pivoting Necessary？ 58

2.7 lutx，bslashtx，lugui 60

2.8 Effect of Roundoff Errors 63

2.9 Norms and Condition Numbers 66

2.10 Sparse Matrices and Band Matrices 72

2.11 PageRank and Markov Chains 74

2.12 Further Reading 81

Exercises 82

3 Interpolation 93

3.1 The Interpolating Polynomial 93

3.2 Piecewise Linear Interpolation 98

3.3 Piecewise Cubic Hermite Interpolation 99

3.4 Shape-Preserving Piecewise Cubic 100

3.5 Cubic Spline 102

3.6 pchiptx，splinetx 105

3.7 interpgui 108

Exercises 110

4 Zeros and Roots 117

4.1 Bisection 117

4.2 Newton’s Method 119

4.3 A Perverse Example 121

4.4 Secant Method 122

4.5 Inverse Quadratic Interpolation 123

4.6 Zeroin 124

4.7 fzerotx，feval 124

4.8 fzerogui 129

4.9 Value Finding and Reverse Interpolation 132

4.10 Optimization and fmintx 132

Exercises 135

5 Least Squares 141

5.1 Models and Curve Fitting 141

5.2 Norms 143

5.3 censusgui 144

5.4 Householder Reflections 145

5.5 The QR Factorization 147

5.6 Pseudoinverse 152

5.7 Rank Deficiency 154

5.8 Separable Least Squares 156

5.9 Further Reading 159

Exercises 159

6 Quadrature 167

6.1 Adaptive Quadrature 167

6.2 Basic Quadrature Rules 168

6.3 quadtx，quadgui 170

6.4 Specifying Integrands 173

6.5 Performance 175

6.6 Integrating Discrete Data 177

6.7 Further Reading 179

Exercises 179

7 Ordinary Differential Equations 187

7.1 Integrating Differential Equations 187

7.2 Systems of Equations 188

7.3 Linearized Differential Equations 189

7.4 Single-Step Methods 191

7.5 The BS23 Algorithm 194

7.6 ode23tx 196

7.7 Examples 199

7.8 Lorenz Attractor 202

7.9 Stiffness 204

7.10 Events 208

7.11 Multistep Methods 212

7.12 The MATLAB ODE Solvers 212

7.13 Errors 213

7.14 Performance 217

7.15 Further Reading 219

Exercises 219

8 Fourier Analysis 237

8.1 Touch-Tone Dialing 237

8.2 Finite Fourier Transform 241

8.3 fftgui 242

8.4 Sunspots 244

8.5 Periodic Time Series 248

8.6 Fast Finite Fourier Transform 249

8.7 ffttx 250

8.8 fftmatrix 251

8.9 Other Fourier Transforms and Series 252

8.10 Further Reading 254

Exercises 254

9 Random Numbers 257

9.1 Pseudorandom Numbers 257

9.2 Uniform Distribution 257

9.3 Normal Distribution 260

9.4 randtx，randntx 263

Exercises 265

10 Eigenvalues and Singular Values 269

10.1 Eigenvalue and Singular Value Decompositions 269

10.2 A Small Example 272

10.3 eigshow 273

10.4 Characteristic Polynomial 275

10.5 Symmetric and Hermitian Matrices 276

10.6 Eigenvalue Sensitivity and Accuracy 277

10.7 Singular Value Sensitivity and Accuracy 283

10.8 Jordan and Schur Forms 284

10.9 The QR Algorithm 285

10.10 eigsvdgui 287

10.11 Principal Components 289

10.12 Circle Generator 293

10.13 Further Reading 298

Exercises 298

11 Partial Differential Equations 307

11.1 Model Problems 307

11.2 Finite Difference Methods 308

11.3 Matrix Representation 310

11.4 Numerical Stability 312

11.5 The L-Shaped Membrane 314

Exercises 319

Bibliography 327

Index 332