Preface to the Second Edition:
This new edition has been updated to include new material. Specifically, this new edition has added sections on the following material:
• Generalized Minimal Residual (GMRES) methods
• Numerical differentiation
• Secant method
• Homotopy and continuation methods
• Power method for computing dominant eigenvalues
• Singular-value decomposition and pseudoinverses
• Matrix pencil method
and a significant revision of the Optimization chapter (Chapter 6) to include linear and quadratic programming methods. A course structure would typically include the following chapters in sequence: Chapter 1, 2, and 3. From this point, any of the chapters can follow without loss of consistency. I have tried to structure each chapter to give the reader an overview of the methods with salient examples. In many cases however, it is not possible to give an exhaustive coverage of the material; many topics have decades of work devoted to their development.
Many of the methods presented in this book have commercial software packages that will accomplish their solution far more rigorously with many failsafe attributes included (such as accounting for ill-conditioning, etc.). It is not my intent to make students experts in each topic, but rather to develop an appreciation for the methods behind the packages.
Many commercial packages provide default settings or choices of parameters for the user; through better understanding of the methods driving the solution, informed users can make better choices and have a better understanding of the situations in which the methods may fail. If this book provides any reader with more confidence in using commercial packages, I have succeeded in my intent. As before, I am indebted to many people: my husband Jim and my children David and Jacob for making every day a joy, my parents Lowell and Sondra for their continuing support, and Frieda Adams for all she does to help me succeed.
Preface to the First Edition:
This book is the outgrowth of a graduate course that I’ve taught at the University of Missouri-Rolla for the past decade or so. Over the years, I’ve used a number of excellent textbooks for this course, but each textbook was always missing some of the topics that I wanted to cover in the class. After relying on handouts for many years, my good friend Leo Grigsby encouraged me to put them down in the form of a book (if arm-twisting can be called encouragement . . . ).
With the support of my graduate students, who I used as testbeds for each chapter, this book gradually came into existence. I hope that those who read this book will find this field as stimulating as I have found it. In addition to Leo and the fine people at CRC Press, I’m grateful to the University of Missouri-Rolla administration and the Department of Electrical and Computer Engineering for providing the environment to nurture my teaching and research and giving me the latitude to pursue my personal interests in this field.
Lastly, I don’t often get the opportunity to publicly acknowledge the people who’ve been instrumental in my professional development. I’d like to thank: Marija Ilic, who initially put me on the path; Peter Sauer, who encouraged me along the way; Jerry Heydt, for providing inspiration; Frieda Adams, for all she does to make my life easier; Steve Pekarek, for putting up with my grumbling and complaining; and Lowell and Sondra Crow for making it all possible.
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