数值分析（第2版）
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四川成都
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作者苏岐芳
出版社中国铁道
ISBN9787113228002
出版时间2017-02
装帧其他
开本16开
定价39.8元
货号9787113228002
上书时间2024-10-20
商品详情
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前言
本书第1 版出版以来，得到了许多专家、同仁及读者的关心、支持和帮助，并提出了许多宝贵意见和建议。借再版之机，首先向关心本书的广大读者、专家、同行和本书的各位责任编辑表示由衷的谢意！
在修订中，为了更适合当前双语教学的需求，我们保留了原教材的系统和编写风格（理论部分以中文为主，软件实现部分以英文为主），注意吸收当前国内外教材改革中一些成功的经验，努力体现创新教学理念，以利于激发学生自主学习，提高实践应用能力，培养综合素质和创新能力。
本次再版修订的内容主要包括以下几方面：
1．订正了语言文字表达方面的不足之处，力求用词规范，表达确切。
2．剔除了个别内容重复和烦琐之处，使理论部分更好地体现“够用为度”的编写原则。
3．恰当地处理有关定理的证明和有关例题的求解方法，使其更加通俗易懂。
4．增补了多重积分、有理逼近、Padé逼近等内容，进一步体现教材的先进性。
5．结合增补内容，对习题配置作了进一步充实、完善。
6．在实验部分，大量增加了算法的Matlab 实现程序及相应的算例，以便于指导学生实践应用。
本书由浙江台州学院苏岐芳副教授主编，浙江台州学院郑学良教授、李希文副教授和应玮婷老师参与修订。具体写作分工为：第1 章、第2 章及附录由李希文修订；第3章由郑学良修订；第4章~第8章由苏岐芳修订；全书的计算机实验由应玮婷修订。
在本书修订过程中，浙江师范大学徐秀斌教授为本书提出了许多宝贵意见，浙江海洋学院郝彦教授、朱玉辉老师及厦门理工学院陈淑萍老师，对本书的编写都做了大量工作，在此一并表示衷心感谢！
编 者
2016年10月
商品简介
本书介绍了科学计算中常用数值分析的基础理论及计算机实现方法。主要内容包括：误差分析、插值、函数逼近、数值积分和数值微分、非线性方程的数值解法、线性方程组的直接解法、线性方程组的迭代解法、常微分方程的数值解法及相应的上机实验内容等。各章都配有大量的习题及上机实验题目，并附有部分习题的参考答案及数学专业软件Mathematica和Matlab的简介。本书采用中、英两种语言编写，适合作为数学、计算机和其他理工类各专业本科“数值分析（计算方法）”双语课程的教材或参考书，也可供从事科学计算的相关技术人员参考。
作者简介
苏岐芳，副教授，台州学院数学与信息工程学院副院长
目录
1 Error Analysis
1.1 Introductio
1.2 Sources of Errors
1.3 Errors and Significant Digits
1.4 Error Propagat
1.5 Qualitative Analysis and Control of Errors
1.5.1 Ill-conditioProblem and ConditioNumber
1.5.2 The Stability of Algorith
1.5.3 The Control of Errors
1.6 Computer Experiments
1.6.1 Functions Needed ithe Experiments by Mathematica
1.6.2 Experiments by Mathematica
1.6.3 Functions Needed ithe Experiments by Matlab
1.6.4 Experiments by Matlab
Exercises 1
2 Interpolating
2.1 Introductio
2.2 Basic Concepts
2.3 Lagrange Interpolatio
2.3.1 Linear and Parabolic Interpolatio
2.3.2 Lagrange InterpolatioPolynomial
2.3.3 InterpolatioRemainder and Error Estimate
2.4 Divided-differences and NewtoInterpolatio
2.5 Differences and NewtoDifference Formulae
2.5.1 Difference
2.5.2 NewtoDifference Formulae
2.6 Hermite Interpolatio
2.7 Piecewise Low Degree Interpolation
2.7.1 Ill-posed Properties of High Degree Interpolatio
2.7.2 Piecewise Linear Interpolatio
2.7.3 Piecewise Cubic Hermite Interpolation
2.8 Cubic Spline Interpolation
2.8.1 Definitioof Cubic Splin
2.8.2 The Constructioof Cubic Spline
2.9 Computer Experiments
2.9.1 Functions Needed ithe Experiments by Mathematica
2.9.2 Experiments by Mathematica
2.9.3 Experiments by Matlab
Exercises 2
3 Best Approximatio
3.1 Introductio
3.2 Norms
3.2.1 Vector Norms
3.2.2 Matrix Norms
3.3 Spectral Radius
3.4 Best Linear Approximatio
3.4.1 Basic Concepts and Theories
3.4.2 Best Linear Approxima
3.5 Discrete Least Squares Approximatio
3.6 Least Squares Approximatioand Orthogonal Polynomials
3.7 Rational FunctioApproxi
3.7.1 Continued Fractions
3.7.2 Padé Approximation
3.8 Computer Experiments
3.8.1 Functions Needed iThe Experiments by Mathematica
3.8.2 Experiments by Mathematica
3.8.3 Functions Needed iThe Experiments by Matlab
3.8.4 Experiments by Matlab
Exercises 3
4 Numerical Integratioand Differentiatio
4.1 Introductio
4.2 Interpolatory Quadratures
4.2.1 Interpolatory Quadrature
4.2.2 Degree of Accuracy
4.3 Newton-Cotes Quadrature Formula
4.4 Composite Quadrature Formul
4.4.1 Composite Trapezoidal Rule
4.4.2 Composite Simpson’s Rule
4.5 Romberg Integration
4.5.1 Recursive Trapezoidal Rule
4.5.2 Romberg Algorithm
4.5.3 Richardson’s Extrapolatio
4.6 GaussiaQuadrature Formula
4.7 Multiple Integrals
4.8 Numerical Differentiation
4.8.1 Numerical Differentiat
4.8.2 DifferentiatioPolynomial Interpolati
4.8.3 Richardson’s Extrapolatio
4.9 Computer Experiments
4.9.1 Functions Needed ithe Experiments by Mathematica
4.9.2 Experiments by Mathematica
4.9.3 Experiments by Matlab
Exercises 4
5 Solutioof Nonlinear Equations
5.1 Introductio
5.2 Basic Theories
5.3 BisectioMet
5.4 Iterative Method and Its Convergence
5.4.1 Fixed Point and Iteratio
5.4.2 Global Convergence
5.4.3 Local Convergence
5.4.4 Order of Convergence
5.5 Accelerating Convergence
5.6 Newton’s Method
5.6.1 Newton’s Method and Its Convergence
5.6.2 Reduced NewtoMethod and Newton’s Descent Method
5.6.3 The Case of Multiple Roots
5.7 Secant Method and Muller Method
5.7.1 Secant Method
5.7.2 Muller Method
5.8 Systems of Nonlinear Equatio
5.9 Computer Experiments
5.9.1 Functions Needed ithe Experiments by Mathematica
5.9.2 Experiments by Mathematica
5.9.3 Experiments by Matlab
Exercises 5
6 Direct Methods for Solving Linear Systems
6.1 Introductio
6.2 GaussiaElimination
6.2.1 Basic GaussiaElimination
6.2.2 Triangular Depositi
6.3 GaussiaEliminatiowith ColumPivoting
6.4 Methods of the Triangular Deposition
6.4.1 The Direct Methods of The Triangular Depositio
6.4.2 The Square Root Method
6.4.3 The Speedup Method
6.5 Analysis of Round-off Errors
6.5.1 ConditioNumber
6.5.2 Iterative Refinement
6.6 Computer Experiments
6.6.1 Functions Needed ithe Experiments by Mathematica
6.6.2 Experiments by Mathematica
6.6.3 Functions Needed ithe Experiments by Matlab
6.6.4 Experiments by Matlab
Exercises 6
7 Iterative Techniques for Solving Linear Systems
7.1 Introductio
7.2 Basic Iterative Methods
7.2.1 Jacobi Method
7.2.2 Gauss-Seidel Method
7.2.3 SOR Method
7.3 Iterative Method Convergence
7.3.1 Basic Theorems
7.3.2 Some Special Systems of Equations
7.4 Computer Experiments
7.4.1 Functions Needed iThe Experiments by Mathematica
7.4.2 Experiments by Mathematica
7.4.3 Experiments by Matlab
Exercises 7
8 Numerical Solutioof Ordinary Differential Equations
8.1 Introductio
8.2 The Existence and Uniqueness of Solutions
8.3 Taylor-Series Method
8.4 Euler’s Method
8.5 Single-step Methods
8.5.1 Single-step Methods
8.5.2 Local TruncatioError
8.6 Runge-Kutta Methods
8.6.1 Second-Order Runge-Kutta Method
8.6.2 Fourth-Order Runge-Kutta Method
8.7 Multistep Methods
8.7.1 General Formulas of Multistep Methods
8.7.2 Adams Explicit and Implicit Formulas
8.8 Systems and Higher-Order Differential Equations
8.8.1 Vector Notatio
8.8.2 Taylor-Series Method for Systems
8.8.3 Fourth-Order Runge-Kutta Formula for Systems
8.9 Computer Experiments
8.9.1 Functions Needed ithe Experiments by Mathematica
8.9.2 Experiments by Mathematica
8.9.3 Experiments by Matlab
Exercises 8
Appendix
Appendix A Mathematica Basic Operations
Appendix B Matlab Basic Operations
Appendix C Answers to Selected Question
Reference
内容摘要
苏岐芳主编的《数值分析（第2版）》介绍了科学计算中常用数值分析的基础理论及计算机实现方法。主要内容包括：误差分析、插值、函数逼近、数值
积分和数值微分、非线性方程的数值解法、线性方程组的直接解法、线性方程组的迭代解法、常微分方程的数值解法及相应的上机实验内容等。各章都配有大量的习题及上机实验题目，并附有部分习题的参考答案及数学专业软件Mathematica和Matlab的简介。
本书采用中、英两种语言编写，适合作为数学、
计算机和其他理工类各专业本科“数值分析（计算方法）”双语课程的教材或参考书，也可供从事科学计算的相关技术人员参考。
主编推荐
数值分析Numerical Analysis（第2版）本书采用中、英两种语言编写，各章都配有大量的习题及上机实验题目，并附有部分习题的参考答案及数学专业软件Mathematica和Matlab的简介。
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