Applied Numerical Methods Using MATLAB. Won Y. Yang

      This book mainly focuses on helping readers understand the fundamental mathematical concepts and practice problem‐solving skills using MATLAB‐based numerical methods, skipping some tedious derivations/proofs. Obviously, basic concepts must be taught so that readers can properly formulate the mathematics problems. Afterward, readers can directly use the MATLAB codes to solve practical problems. Almost every algorithm introduced in this book is followed by example MATLAB code with a friendly interface so that students can easily modify the code to solve their own problems. The selection of exercises follows the same philosophy of making the learning easy and practical. Readers should be able to solve similar problems immediately after reading the materials and codes listed in this book. For most students – and particularly non‐math majors – understanding how to use numerical tools correctly in solving their problems of interest is more important than doing lengthy proofs and derivations.

MATLAB is one of the most developed software packages available today. It provides many numerical methods and it is very easy to use, even for those having no programming technique or experience. We have supplemented MATLAB's built‐in functions with over 100 small MATLAB routines. Readers should find these routines handy and useful. Some of these routines give better results for some problems than the built‐in functions. Readers are encouraged to develop their own routines following the examples.

      Compared with the first edition, Bairstow's method (Section 4.7), Integration Involving PWL Function (Section 5.11), Mixed Integer Linear Programming (Section 7.3.4), Neural Network (Section 7.4), Adaptive Filter (Section 7.5), Recursive Least‐Squares Estimation (Section 7.6), and DoA Estimation (Section 8.8) have been added to the second edition.

      Program files can be downloaded from <https://wyyang53.wixsite.com/mysite/publications>. Any questions, comments, and suggestions regarding this book are welcome and they should be mailed to [email protected].

      Won Y. Yang et al.

      March 2020

Acknowledgments

      The knowledge in this book is derived from the work of many eminent scientists, scholars, researchers, and MATLAB developers, all of whom we thank. We thank our colleagues, students, relatives, and friends for their support and encouragement. We thank the reviewers, whose comments were so helpful in tuning this book. We gratefully acknowledge the editorial, Brett Kurzman and production staff of John Wiley & Sons, Inc. including Project Editor Antony Sami and Production Editor Gayathree Sekar for their kind, efficient, and encouraging guide.

About the Companion Website

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       Learning Outcomes for all chapters

       Exercises for all chapters

       References for all chapters

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       Figures for chapters 16, 22 and 30

1 MATLAB Usage and Computational Errors

      Chapter Outline

        1.1 Basic Operations of MATLAB 1.1.1 Input/Output of Data from MATLAB Command Window 1.1.2 Input/Output of Data Through Files 1.1.3 Input/Output of Data Using Keyboard 1.1.4 Two‐Dimensional (2D) Graphic Input/Output 1.1.5 Three Dimensional (3D) Graphic Output 1.1.6 Mathematical Functions 1.1.7 Operations on Vectors and Matrices 1.1.8 Random Number Generators 1.1.9 Flow Control

        1.2 Computer Errors vs. Human Mistakes 1.2.1 IEEE 64‐bit Floating‐Point Number Representation 1.2.2 Various Kinds of Computing Errors 1.2.3 Absolute/Relative Computing Errors 1.2.4 Error Propagation 1.2.5 Tips for Avoiding Large Errors

        1.3 Toward Good Program 1.3.1 Nested Computing for Computational Efficiency 1.3.2 Vector Operation vs. Loop Iteration 1.3.3 Iterative Routine vs. Recursive Routine 1.3.4 To Avoid Runtime Error 1.3.5 Parameter Sharing via GLOBAL Variables 1.3.6 Parameter Passing Through VARARGIN 1.3.7 Adaptive Input Argument List Problems

1.1 Basic Operations of MATLAB

MATLAB is a high‐level software package with many built‐in functions that make the learning of numerical methods much easier and more interesting. In this section, we will introduce some basic operations that will enable you to learn the software and build your own programs for problem solving. In the workstation environment, you type “matlab” to start the program, while in the PC environment, you simply double‐click the MATLAB icon.

      Once you start the MATLAB program, a Command window will open with the MATLAB prompt ≫. On the command line, you can type MATLAB commands, functions together with their input/output arguments, the names of script files containing a block of statements to be executed at a time or functions defined by users. The MATLAB program files must have the extension name ***.m to be executed in the MATLAB environment. If you want to create a new M‐file or edit an existing file, you click File/New/M‐file or File/Open in the top left corner of the main menu, find/select/load the file by double‐clicking it, and then begin editing it in the Editor window. If the path of the file you want to run is not listed in the MATLAB search path, the file name will not be recognized by MATLAB. In such cases, you need to add the path to the MATLAB‐path list by clicking the menu ‘Set_Path’