MATLAB数值计算（英文版 2013修订版）

Preface 1Introduction to MATLAB 1.1 The Golden Ratio 1.2 Fibonacci Numbers 1.3 Fractal Fern 1.4 Magic Squares 1.5 Cryptography 1.6 The 3n+1 Sequence 1.7 Floating-Point Arithmetic 1.8 Further Reading Exercises 2 Linear Equations 2.1 Solving Linear Systems 2.2 The MATLAB Backslash Operator 2.3 A 3-by-3 Example 2.4 Permutation and Triangular Matrices 2.5 LU Factorization 2.6 Why Is Pivoting Necessary? 2.7 lutx, bslashtx, lugui 2.8 Effect of Roundoff Errors 2.9 Norms and Condition Numbers 2.10 Sparse Matrices and Band Matrices 2.11 PageRank and Markov Chains 2.12 Further Reading Exercises 3 Interpolation 3.1 The Interpolating Polynomial 3.2 Piecewise Linear Interpolation 3.3 Piecewise Cubic Hermite Interpolation 3.4 Shape-Preserving Piecewise Cubic 3.5 Cubic Spline 3.6 pchiptx, splinetx 3.7 interpgui Exercises 4 Zeros and Roots 4.1 Bisection 4.2 Newton's Method 4.3 A Perverse Example 4.4 Secant Method 4.5 Inverse Quadratic Interpolation 4.6 Zeroin 4.7 fzerotx 4.8 fzerogui 4.9 Value Finding and Reverse Interpolation 4.10 Optimization and fmintx Exercises 5 Least Squares 5.1 Models and Curve Fitting 5.2 Norms 5.3 censusgui 5.4 Householder Reflections 5.5 The QR Factorization 5.6 Pseudoinverse 5.7 Rank De ciency 5.8 Separable Least Squares 5.9 Further Reading Exercises 6 Quadrature 6.1 Adaptive Quadrature 6.2 Basic Quadrature Rules 6.3 quadtx, quadgui 6.4 Specifying Integrands 6.5 Performance 6.6 Integrating Discrete Data 6.7 Further Reading Exercises 7 Ordinary Differential Equations 193 7.1 Integrating Differential Equations 7.2 Systems of Equations 7.3 Linearized Differential Equations 7.4 Single-Step Methods 7.5 The BS23 Algorithm 7.6 ode23tx 7.7 Examples 7.8 Lorenz Attractor 7.9 Stiffness 7.10 Events 7.11 Multistep Methods 7.12 The MATLAB ODE Solvers 7.13 Errors 7.14 Performance 7.15 Further Reading Exercises 8 Fourier Analysis 8.1 Touch-Tone Dialing 8.2 Finite Fourier Transform 8.3 fftgui 8.4 Sunspots 8.5 Periodic Time Series 8.6 Fast Finite Fourier Transform 8.7 ffttx 8.8 fftmatrix 8.9 Other Fourier Transforms and Series 8.10 Further Reading Exercises