MATLAB数值方法入门教程（第四版）

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"An Introduction to Numerical Methods A MATLAB Approach, 4th Edition" 是一本由Dr. Abdelwahab Kharab和Professor Ronald B. Guenther合著的关于数值方法的书籍，出版于2019年，由CRC Press（Taylor & Francis Group的印记）发行。这本书使用MATLAB作为工具来介绍和讲解数值方法。本书的核心知识点包括： 1. **数值方法基础**：书中可能涵盖了数值方法的基本概念，如插值、拟合、微积分近似、数值积分和微分方程的数值解法等。这些基本方法是所有数值分析的基础，对理解和解决实际工程和科学问题至关重要。 2. **MATLAB编程**：作者通过MATLAB这一强大的数学计算软件来阐述数值方法，读者可以学习如何利用MATLAB编写代码来实现各种数值算法，如线性代数问题的求解、非线性方程的迭代解法等。 3. **误差分析**：书中可能会讨论数值方法中的误差来源，如舍入误差和截断误差，以及如何分析和控制这些误差，这对于确保数值结果的准确性和可靠性是必不可少的。 4. **数值线性代数**：可能包括矩阵运算、特征值问题、奇异值分解、LU分解、QR分解等线性代数中的数值方法，这些都是数值分析和科学计算中的核心部分。 5. **微分方程的数值解**：可能涵盖了欧拉方法、龙格-库塔方法等常微分方程的数值解法，以及有限差分和有限元方法等偏微分方程的近似解法，这些都是处理动态系统和物理问题的关键工具。 6. **优化与最优化**：书中可能涉及一维搜索、梯度下降法、牛顿法等数值优化算法，这些在工程设计、机器学习等领域广泛应用。 7. **数值实验与案例研究**：通过实例来展示如何将理论知识应用到实际问题中，可能是通过MATLAB编程实现并分析结果，提升读者的实践能力。 8. **代码调试与验证**：强调了如何验证数值程序的正确性，包括边界条件的设定、初始值的选择以及结果的合理性检验。 9. **最新发展与应用**：由于是第四版，书中的内容可能包含近年来数值方法的新进展和MATLAB的最新版本特性，使读者能够了解该领域的前沿动态。通过阅读本书，读者不仅可以掌握数值方法的基本理论，还能获得使用MATLAB解决实际问题的实战经验，这对于从事科学计算、工程设计、数据分析等相关工作的专业人士来说是非常宝贵的资源。

Preface xv

Acknowledgments

We wish to thank the many persons who have helped us in the creation of this

book. They are:

From Abu Dhabi University, Dr. Deena Elsori, Dr. Jamal Benbourenane, Dr.

Makhtar Sarr, Prof. Haydar Akca and Prof. Hichem Eleuch. Mr. Saadaoui Mo-

hamed from University of Laghouat.

Special thanks are due to those who gave their time to edit our book, Mr. Zack

Polaski and Mr. Faysel Kharab from Lisbon University.

The authors remain very grateful to Sarfraz Khan and the editorial and pro-

duction staﬀ of Chapman & Hall/CRC who have been helpful and available at all

stages.

Finally, the authors are grateful for the ﬁnancial and facilities support provided

by Dr. Ashraf Khalil Director of Research of Abu Dhabi University.

Suggestions for improvements to the book are always welcome and can be made

by e-mail at: awkharab@yahoo.com.

Abdelwahab Kharab

Ronald B. Guenther

Chapter 1

Introduction

The Taylor Series is one of the most important tools in numerical analysis. It

constitutes the foundation of numerical methods and will be used in most of the

chapters of this text. From the Taylor Series, we can derive the formulas and error

estimates of the many numerical techniques used. This chapter contains a review

of the Taylor Series, and a brief introduction to MATLAB



1.1 ABOUT MATLAB and MAT LA B GUI (Graphical User Inter-

face)

MATLAB (MATrix LABoratory) is a powerful interactive system for matrix-

based computation designed for scientiﬁc and engineering use. It is good for many

forms of numeric computation and visualization. MATLAB language is a high-

level matrix/array language with control ﬂow statements, functions, data structures,

input/output, and object-oriented programming features. To fully use the power

and computing capabilities of this software program in classrooms and laboratories

by teachers and students in science and engineering, part of this text is intended to

introduce the computational power of MATLAB to modern numerical methods.

MATLAB has several advantages. There are three major elements that have

contributed to its immense popularity. First, it is extremely easy to use since

data can be easily entered, especially for algorithms that are adaptable to a table

format. This is an important feature because it allows students to experiment

with many numerical problems in a short period of time. Second, it includes high-

level commands for two-dimensional and three-dimensional data visualization, and

presentation graphics. Plots are easily obtained from within a script or in command

mode. Third, the most evident power of a MATLAB is its speed of calculation.

The program gives instantaneous feedback. Because of their popularity, MATLAB

and other software such as MAPLE and Mathematica are now available in most

university microcomputer laboratories.

One of the primary objectives of this text is to give students a clear step-by-step

explanation of the algorithm corresponding to each numerical method used. To

accomplish this objective, we have developed MATLAB M-functions contained in

2 INTRODUCTION

a supplementary CD-ROM at the back of the book. These M-ﬁles can be used for

the application or illustration of all numerical methods discussed in this text. Each

M-function will enable students to solve numerical problems simply by entering data

and executing the M-functions.

It is well known that the best way to learn computer programming is to write

computer programs. Therefore, we believe that by understanding the basic theory

underlying each numerical method and the algorithm behind it, students will have

the necessary tools to write their own programs in a high-level computer language

such as C or FORTRAN.

Another future of MATLAB is that it provides the Graphical User Interface

(GUI). It is a pictorial interface to a program intended to provide students with

a familiar environment in which to work. This environment contains push buttons,

toggle buttons, lists, menus, text boxes, and so forth, all of which are already famil-

iar to the user, so that they can concentrate on using the application rather than on

the mechanics involved in doing things. They do not have to type commands at the

command line to run the MATLAB functions. For this reason, we introduced GUI

in this edition to make it easier for the students to run the M-functions of the book.

A readme ﬁle named ”SUN Package readme contained in the directory NMETH”

of the CD attached at the back cover of the book, explains in details the steps to

follow to run the MATLAB functions using GUI. In addition, Appendix D shows

the use of GUI for solving several examples.

1.2 AN INTRODUCTION TO MATLAB

In this section we give to the reader a brief tutorial introduction to MATLAB.

For additional information we urge the reader to use the reference and user’s guides

of MATLAB.

1.2.1 Matrices and matrix computation

MATLAB treats all variables as matrices. They are assigned to expressions by

using an equal sign and their names are case-sensitive. For example,

>> A = [4 -2 5; 6 1 7; -1 0 6]

A =

4 −2 5

6 1 7

−1 0 6

New rows may be indicated by a new line or by a semicolon. A column vector

may be given as

>> x = [2; 8; 9] or x = [2 8 9]’

x =

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