Book Details :
Title : Numerical Linear Algebra and Optimization, Vol. 1
Author : Philip E. Gill, Walter Murray, Margaret H. Wright
Hardcover : 448 pages
Publisher : Perseus Books (Sd) (September 1990)
Language : English
ISBN-10 : 0201126494
ISBN-13 : 978-0201126495
Size : 4.65 MB.
Type : Pdf.
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Book Description :

Our intent in writing this book is to provide a unified introduction for students and practitioners to three distinct but closely related areas:
1. Fundamentals of numerical analysis and scientific computing;
2. Techniques for solving linear systems and linear least-squares problems, and for updating matrix factorizations;
3. Numerical optimization methods for both linear and nonlinear programming.

These topics not only form a coherent body of knowledge for pedagogical purposes, but are also important background for anyone who wishes to understand and develop numerical methods and software. Unfortunately, they are rarely taught together. Introductory treatments of numerical analysis and scientific computing often do not mention optimization at all, or else refer to an extremely limited set of problem categories and methods.

Textbooks on linear algebra typically do not discuss techniques for updating matrix factorizations, which have become an essential part of modern linear algebra and optimization during the last 20 years. Finally, many books on optimization, particularly those on linear programming, include little if any discussion of numerical analysis.

In this book, a self-contained and consistent presentation is given of the three areas listed above. The level of difficulty is designed for those with basic knowledge of multivariate calculus and linear algebra, although most of the relevant background is summarized in the text. Some elementary knowledge of computer science is helpful in understanding the "pseudo-code" form of algorithms. The book is likely to be most useful for advanced undergraduate or masters-level courses, but could also be used to teach selected material for students at the Ph.D. level.

The book was started in 1987 to accompany a new course on "Scientific Computing and Numerical Optimization" in the Department of Operations Research at Stanford University. In the intervening years, various versions of the book have been used by the authors to teach both undergraduate and graduate courses at Stanford University, the University of California at San Diego, and Princeton University.

The progression of topics in Volumes 1 and 2 is designed to correspond to an intensive one-year course in numerical linear algebra and optimization, starting with linear algebra and working through nonlinearly constrained optimization. The topics also fit into other standard course sequences.

Volume 1 contains more than 200 exercises with a wide range of difficulty. Since students learn about the non-obvious complexities of computation only from their own experience, we have formulated a substantial number of the homework problems so that they may be solved with an interactive package for matrix calculations. Several such packages are already widely available—in particular, MATLAB™and Mathematica™. The ability to perform nontrivial calculations expressed in a natural form creates understanding of what "really happens" in numerical computation. (Without such a package, numerical exercises tend to be designed mainly to make the arithmetic simple rather than to present the relevant concepts.)

At the end of each chapter, we suggest further reading intended to provide more detailed coverage of the relevant topics. To avoid the impossible task of compiling even a marginally complete list of research papers, we have chosen to cite only books, with the occasional exception of research papers that have directly influenced our presentation.