MATLAB数值计算

Preface

1 Introduction 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+l 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

Preface

1 Introduction 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+l 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 fzerctx

4.8 fzeregui

4.9 Value Finding and Reverse Interpolation

4.10 Optimization and fmintx

Exercises

5 Least Squares

5.1 Models and Curve Fitting

5.2 Ncrms

5.3 censusgui

5.4 Householder Reflections

5.5 The QR Factorization

5.6 Pseu doinverse

5.7 Rank Deficiency

5.8 Separable Least Squares

5.9 b-hrther Reading

Exercises

6 Quadrature

6.1 Adaptive Quadrature

6.2 Basic Quadrature Rules

6.3 qusdtx, quadgui

6.4 Specifying Integrands

6.5 Performance

6.6 Integrating Discrete Data

6.7 Further Reading

Exelcises

7 Ordinary Differential Equations

7.1 Integrating Differential Equations

7.2 Systems of Equations

7.3 Lineari2ed 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

9 Random Numbers

9.1 Pseudorandom Numbers

9.2 Uniform Distribution

9.3 Normal Distribution

9.4 randtx, randntx

9.5 Twister

Exercises

10 Eigenvalues and Singular Values

10.1 Eigenvalue and Singular Value Decompositions

10.2 A Small Example

10.3 eigshow

10.4 Characteristic Polynomial

10.5 Symmetric and Hermitian Matrices

10.6 Eigenvalue Sensitivity and Accuracy

10.7 Singular Value Sensitivity and Accuracy

10.8 Jordan and Schur Forms

10.9 The QR Algorithm

10.10 eigsvdgui

10.11 Principal Components

10.12 Circle Generator

10.13 Further Reading

Exercises

11 Partial Differential Equations

11.1 Model Problems

11.2 Finite Difference Methods

11.3 Matrix Representation

11.4 Numerical Stability

11.5 The L-Shaped Membrane

Exercises

Bibliography

Index

莫勒的《MATLAB数值计算（2013修订版英文版）》 风格生动，适用于数值方法、MATLAB 和技术计算等 方面的初级课程，着重介绍数学软件的熟练使用及其 内在的高效率算法。主要内容包括：MATLAB介绍、线 性方程组、插值、方程求根、最小二乘法、数值积分 、常微分方程、傅里叶分析、随机数、特征值与奇异 值、偏微分方程。

本书中文版购买链接：MATLAB数值计算(Numerical Computing with MATLAB 中译本，最新修订)





MATLAB创始人Cleve B. Moler原创作品4本，畅销英文原著，权威中文编译：