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科学计算导论（第2版）
作者：（美）Michael T.Heath著
出版社：清华大学出版社
出版时间：2001-10-01
ISBN：9787302049005
定价：¥55.00
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内容简介
本书全面的介绍了科学计算中解各种主要问题的数值方法，包括线性和非线性方程，最小二乘法，特征值，最优化，插值，积分，常微分方程和偏微分方程，快速傅立叶变换和随机数生成。本书的特点是：**以使用算法的读者为对象，重点讲授算法背后的思想和原理，而不是算法的详细分析。**强调敏感性和病态性等概念，对同一问题的不同算法进行比较和评价，提高读者对算法的鉴赏能力。**对每类问题都专门介绍和讨论有关的数学软件，包括在Internet上可以获得的免费软件和有版权保护的商业软件平台，供读者选用。**丰富的例题和习题，书中包括169道例题，500多道思考题，240多道练习题和200多道数值计算题。本书可作为研究生“数值分析”课程的教材或参考书，对于需要解决计算问题的科技人员，本书具有很高的参考价值。
作者简介
暂缺《科学计算导论（第2版）》作者简介
目录
Preface
Notation
1 Scientific Computing
1.1 Introduction
1.2 Approximations in Scientific Computation
1.3 Computer Arithmetic
1.4 Mathematical Software
1.5 Historical Notes and Further Reading
2 Systems of Linear Equations
2.1 Linear Systems
2.2 Existence and Uniqueness
2.3 Sensitivity and Conditioning
2.4 Solving Linear Systems
2.5 Special Types of Linear Systems
2.6 Iterative Methods for Linear Systems
2.7 Software for Linear Systems
2.8 Historical Notes and Further Reading
3 Linear Least Squares
3.1 Linear Least Squares Problems
3.2 Existence and Uniqueness
3.3 Sensitivity and Conditioning
3.4 Problem Transformations
3.5 Orthogonalization Methods
3.6 Singular Value Decomposition
3.7 Comparison of Methods
3.8 Software for Linear Least Squares
3.9 Historical Notes and Further Reading
4 Eigenvalue Problems
4.1 Eigenvalues and Eigenvectors
4.2 Existence and Uniqueness
4.3 Sensitivity and Conditioning
4.4 Problem Transformations
4.5 Computing Eigenvalues and Eigenvectors
4.6 Generalized Eigenvalue Problems
4.7 Computing the Singular Value Decomposition
4.8 Software for Eigenvalue Problems
4.9 Historical Notes and Further Reading
5 Nonlinear Equations
5.1 Nonlinear Equations
5.2 Existence and Uniqueness
5.3 Sensitivity and Conditioning
5.4 Convergence Rates and Stopping Criteria
5.5 Nonlinear Equations in One Dimension
5.6 Systems of Nonlinear Equations
5.7 Software for Nonlinear Equations
5.8 Historical Notes and Farther Reading
6 Optimization
6.1 Optimization Problems
6.2 Existence and Uniqueness
6.3 Sensitivity and Conditioning
6.4 Optimization in One Dimension
6.5 Unconstrained Optimization
6.6 Nonlinear Least Squares
6.7 Constrained Optimization
6.8 Software for Optimization
6.9 Historical Notes and Further Reading
7 Interpolation
7.1 Interpolation
7.2 Existence, Uniqueness, and Conditioning
7.3 Polynomial Interpolation
7.4 Piecewise Polynomial Interpolation
7.5 Software for Interpolation
7.6 Historical Notes and Further Reading
8 Numerical Integration and Differentiation
8.1 Integration
8.2 Existence, Uniqueness, and Conditioning
8.3 Numerical Quadrature
8.4 Other Integration Problems
8.5 Integral Equations
8.6 Numerical Differentiation
8.7 Richardson Extrapolation
8.8 Software for Integration and Differentiation
8.9 Historical Notes and Further Reading
9 Initial Value Problems for ODEs
9.1 Ordinary Differential Equations
9.2 Existence, Uniqueness, and Conditioning
9.3 Numerical Solution of ODES
9.4 Software for ODE Initial Value Problems
9.8 Historical Notes and Further Reading
10 Boundary Value Problems for ODEs
10.1 Boundary Value Problems
10.2 Existence, Uniqueness, and Conditioning
10.3 Shooting Method
10.4 Finite Difference Method
10.5 Collocation Method
10.6 Galerkin Method
10.7 Eigenvalue Problems
10.8 Software for ODE Boundary Value Problems
10.9 Historical Notes and Further Reading
11 Partial Differential Equations
11.1 Partial Differential Equations
11.2 Time-Dependent Problems
11.3 Time-Independent Problems
11.4 Direct Methods for Sparse Linear Systems
11.5 Iterative Methods for Linear Systems
11.6 Comparison of Methods
11.7 Software for Partial Differential Equations
11.8 Historical Notes and Further Reading
12 Fast Fourier Transform
12.1 Trigonometric Interpolation
12.2 FFT Algorithm
12.3 Applications of DFT
12.4 Wavelets
12.5 Software for FFT
12.6 Historical Notes and Further Reading
13 Random Numbers and Simulation
13.1 Stochastic Simulation
13.2 Randomness and Random Numbers
13.3 Random Number Generators
13.4 Quasi-Random Sequences
13.5 Software for Generating Random Numbers
13.6 Historical Notes and Further Reading
Bibliography
Index
Notation
1 Scientific Computing
1.1 Introduction
1.2 Approximations in Scientific Computation
1.3 Computer Arithmetic
1.4 Mathematical Software
1.5 Historical Notes and Further Reading
2 Systems of Linear Equations
2.1 Linear Systems
2.2 Existence and Uniqueness
2.3 Sensitivity and Conditioning
2.4 Solving Linear Systems
2.5 Special Types of Linear Systems
2.6 Iterative Methods for Linear Systems
2.7 Software for Linear Systems
2.8 Historical Notes and Further Reading
3 Linear Least Squares
3.1 Linear Least Squares Problems
3.2 Existence and Uniqueness
3.3 Sensitivity and Conditioning
3.4 Problem Transformations
3.5 Orthogonalization Methods
3.6 Singular Value Decomposition
3.7 Comparison of Methods
3.8 Software for Linear Least Squares
3.9 Historical Notes and Further Reading
4 Eigenvalue Problems
4.1 Eigenvalues and Eigenvectors
4.2 Existence and Uniqueness
4.3 Sensitivity and Conditioning
4.4 Problem Transformations
4.5 Computing Eigenvalues and Eigenvectors
4.6 Generalized Eigenvalue Problems
4.7 Computing the Singular Value Decomposition
4.8 Software for Eigenvalue Problems
4.9 Historical Notes and Further Reading
5 Nonlinear Equations
5.1 Nonlinear Equations
5.2 Existence and Uniqueness
5.3 Sensitivity and Conditioning
5.4 Convergence Rates and Stopping Criteria
5.5 Nonlinear Equations in One Dimension
5.6 Systems of Nonlinear Equations
5.7 Software for Nonlinear Equations
5.8 Historical Notes and Farther Reading
6 Optimization
6.1 Optimization Problems
6.2 Existence and Uniqueness
6.3 Sensitivity and Conditioning
6.4 Optimization in One Dimension
6.5 Unconstrained Optimization
6.6 Nonlinear Least Squares
6.7 Constrained Optimization
6.8 Software for Optimization
6.9 Historical Notes and Further Reading
7 Interpolation
7.1 Interpolation
7.2 Existence, Uniqueness, and Conditioning
7.3 Polynomial Interpolation
7.4 Piecewise Polynomial Interpolation
7.5 Software for Interpolation
7.6 Historical Notes and Further Reading
8 Numerical Integration and Differentiation
8.1 Integration
8.2 Existence, Uniqueness, and Conditioning
8.3 Numerical Quadrature
8.4 Other Integration Problems
8.5 Integral Equations
8.6 Numerical Differentiation
8.7 Richardson Extrapolation
8.8 Software for Integration and Differentiation
8.9 Historical Notes and Further Reading
9 Initial Value Problems for ODEs
9.1 Ordinary Differential Equations
9.2 Existence, Uniqueness, and Conditioning
9.3 Numerical Solution of ODES
9.4 Software for ODE Initial Value Problems
9.8 Historical Notes and Further Reading
10 Boundary Value Problems for ODEs
10.1 Boundary Value Problems
10.2 Existence, Uniqueness, and Conditioning
10.3 Shooting Method
10.4 Finite Difference Method
10.5 Collocation Method
10.6 Galerkin Method
10.7 Eigenvalue Problems
10.8 Software for ODE Boundary Value Problems
10.9 Historical Notes and Further Reading
11 Partial Differential Equations
11.1 Partial Differential Equations
11.2 Time-Dependent Problems
11.3 Time-Independent Problems
11.4 Direct Methods for Sparse Linear Systems
11.5 Iterative Methods for Linear Systems
11.6 Comparison of Methods
11.7 Software for Partial Differential Equations
11.8 Historical Notes and Further Reading
12 Fast Fourier Transform
12.1 Trigonometric Interpolation
12.2 FFT Algorithm
12.3 Applications of DFT
12.4 Wavelets
12.5 Software for FFT
12.6 Historical Notes and Further Reading
13 Random Numbers and Simulation
13.1 Stochastic Simulation
13.2 Randomness and Random Numbers
13.3 Random Number Generators
13.4 Quasi-Random Sequences
13.5 Software for Generating Random Numbers
13.6 Historical Notes and Further Reading
Bibliography
Index
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