Product Description

Designed for use by first-year graduate students from a variety of engineering and scientific disciplines, this comprehensive textbook covers the solution of linear systems, least squares problems, eigenvalue problems, and the singular value decomposition. The author, who helped design the widely used LAPACK and ScaLAPACK linear algebra libraries, draws on this experience to present state-of-the-art techniques for these problems, including recommendations of which algorithms to use in a variety of practical situations.

If you are looking for a textbook that - teaches state-of-the-art techniques for solving linear algebra problems, - covers the most important methods for dense and sparse problems, - presents both the mathematical background and good software techniques, - is self-contained, assuming only a good undergraduate background in linear algebra,

then this is the book for you.

Algorithms are derived in a mathematically illuminating way, including condition numbers and error bounds. Direct and iterative algorithms, suitable for dense and sparse matrices, are discussed. Algorithm design for modern computer architectures, where moving data is often more expensive than arithmetic operations, is discussed in detail, using LAPACK as an illustration. There are many numerical examples throughout the text and in the problems at the ends of chapters, most of which are written in Matlab and are freely available on the Web.

Material either not available elsewhere, or presented quite differently in other textbooks, includes - a discussion of the impact of modern cache-based computer memories on algorithm design; - frequent recommendations and pointers in the text to the best software currently available, including a detailed performance comparison of state-of-the-art software for eigenvalue and least squares problems, and a description of sparse direct solvers for serial and parallel machines; - a discussion of iterative methods ranging from Jacobi's method to multigrid and domain decomposition, with performance comparisons on a model problem; - a great deal of Matlab-based software, available on the Web, which either implements algorithms presented in the book, produces the figures in the book, or is used in homework problems; - numerical examples drawn from fields ranging from mechanical vibrations to computational geometry; - high-accuracy algorithms for solving linear systems and eigenvalue problems, along with tighter "relative" error bounds; - dynamical systems interpretations of some eigenvalue algorithms.

Demmel discusses several current research topics, making students aware of both the lively research taking place and connections to other parts of numerical analysis, mathematics, and computer science. Some of this material is developed in questions at the end of each chapter, which are marked Easy, Medium, or Hard according to their difficulty. Some questions are straightforward, supplying proofs of lemmas used in the text. Others are more difficult theoretical or computing problems. Questions involving significant amounts of programming are marked Programming. The computing questions mainly involve Matlab programming, and others involve retrieving, using, and perhaps modifying LAPACK code from NETLIB.

Product Details

• Amazon Sales Rank: #538709 in Books
• Published on: 1997-08-01
• Format: Illustrated
• Original language: English
• Number of items: 1
• Binding: Paperback
• 431 pages

Review
I have used Numerical Linear Algebra in my introductory graduate course and I have found it to be almost the perfect text to introduce mathematics graduate students to the subject. I like the choice of topics and the format: a sequence of lectures. Each chapter (or lecture) carefully builds upon the material presented in previous chapters, providing new concepts in a very clear manner. Exercises at the end of each chapter reinforce the concepts, and in some cases introduce new ones. …The emphasis is on the mathematics behind the algorithms, in the understanding of why the algorithms work. …The text is sprinkled with examples and explanations, which keep the student focused. --Daniel B. Szyld, Department of Mathematics, Temple University.

Just exactly what I might have expected--an absorbing look at the familiar topics through the eyes of a master expositor. I have been reading it and learning a lot. --Paul Saylor, University of Illinois at Urbana-Champaign

This is a beautifully written book which carefully brings to the reader the important issues connected with the computational issues in matrix computations. The authors show a broad knowledge of this vital area and make wonderful connections to a variety of problems of current interest. The book is like a delicate soufflé --- tasteful and very light. --Gene Golub, Stanford University.

Review
‘If you do any computing with matrices - including linear systems, least squares, and eigenvalues - this book cannot but help you understand what you are doing and why. It presents state-of-the-art material (as of June 1997) and can serve as a text or a reference…’ L. Ehrlich, Randallstown, MD, Computing Reviews

‘…This book is a friendly treatment of numerical linear algebra tailored to first-year graduate students from a variety of engineering and scientific disciplines. The treatment of rounding error analysis and perturbation theory is exceptionally thorough and careful … The author's writing style is very clear and a pleasure to read.’ William W. Hager, Mathematical Reviews

‘…The disposition is very much like a series of lectures, new concepts are introduced precisely where needed … Illustrating examples are given, some reporting really heavy computations, but the author does not shy away from giving mathematical proofs where that is needed …’ A. Ruhe, Zeitschrift fur Mathematik und ihre Grenzgebiete

‘…Compare Demmel with the standard work by G. Golub and C. Van Loan, Matrix Computations (3rd ed., 1996) … Demmel offers a smaller number of topics but focuses on the most important, and provides a more readable introduction for beginners.’ B. Borchers, CHOICE

‘… highly recommended to graduate students in the field and a must for university libraries. Students will enjoy the gradual introduction to problems clearly marked as Easy, Medium, or Hard according to their level of difficulty. Readers will benefit from reading the preface to acquaint themselves with the philosophy that guided the author while writing the book.’ L. Y. Bahar, Applied Mechanics Review

"Jim Demmel's book on applied numerical linear algebra is a wonderful text blending together the mathematical basis, good numerical software, and practical knowledge for solving real problems. It is destined to be a classic." -Jack Dongarra, Department of Computer Science, University of Tennessee, Knoxville.

"This book has many unprecedented features as a graduate textbook and research reference book on numerical linear algebra and matrix computations. Many topics appear for the first time in a graduate textbook, such as single precision iterative refinement, relative perturbation theory, full-version of divide-and-conquer method, high precision Jacobi method, connection of QR method and the Toda lattice and so on. …It is astonishing to what extent this book, by means of systematic and easily understandable exposition, has succeeded in making clear the state of the art of numerical linear algebra theory, methods and analysis which we numerical analysts consider the lively frontier of our current work." -Zhaojun Bai, University of Kentucky.

"This is an excellent graduate-level textbook for people who want to learn or teach the state of the art of numerical linear algebra. It covers systematically all the fundamental topics in theory, as well as software implementation. The book is very easy to use in the classroom since it provides pointers, in the book and on the author's home page, to lots of available Matlab and LAPACK routines, and it has a large number of homework problems marked with Easy, Medium and Hard. The book requires the students to have a stronger background in linear algebra than most other engineering books on numerical linear algebra." -Xia-Chuan Cai, Department of Computer Science, University of Colorado.

"Demmel's book covers the state of the art tools of numerical linear algebra. He tells us how they work and why they work so well. He also gives many references to recent research work. … he avoids including everything, so the book is still easy to read. …" -Martin H. Gutknecht, IPS Supercomputing in Zurich, Switzerland.

About the Author
James Demmel is a Professor in the Computer Science Division and Mathematics Department at the University of California, Berkeley. He was elected to the National Academy of Engineering in 1999.

Customer Reviews

Excellent: the best book I have seen on the subject.
This book should be required reading for anyone interested in computational numerics, especially those who are starting in the field. The authors concentrate on the few fundamental topics that underlie and unite the subject. The presentation, while rigorous, is simple, clear and friendly. The authors follow a logical thread and eliminate unnecessary and disorienting aspects that plague other books on the subject. It is easy to pick up the book, read several chapters at a stretch without looking up, and come away with new insights. Unquestionably the most valuable book I have read to date on the subject.

This book grows on you
I used this text for a two-semester graduate sequence in numerical linear algebra (NLA) while I was a graduate student in the Mathematics Department at The University of Kentucky. If you do not have a substantial background in linear algebra and numerical analysis, which I did not when I first used this book, the material covered and the presentation can seem to be quite daunting. But while the presentation is very thorough, it is not unnecessarily so. After I had used this text for about three months, I grew accustomed to the very detailed nature of the writing and grateful for the sheer level of information contained in a meer 419 pages.

Many introductury numerical analysis books include several chapters covering the commonly used algorithms in NLA but usually not in complete detail. While this format is friendlier to use for an overview of the "basics," in the real world, the standard ways of solving numerical systems such as GEPP, SVD, QR, Cholesky decompostions, Gauss-Siedel iterations, and other methods do not always work in a nice cookbook-like fashion. When one of these standard methods that engineers and research scientists use to solve "standard" problems fails, and it will sometimes, this book will give you a good starting point to figure out what went wrong and what alternate methods can be used to solve a linear system that is not as easy as it first appeared to be.

If you are learning NLA, you are probably doing so because you either want to or have to apply it in your professional life, by which I mean your job or the job that you hope to get. In my current position, I develop and design statistical and deterministic simulators for human genetics research. And when I need to used Cholesky decompostions, SVD's, and other NLA methods, I always consult this book to review how these methods work and, more importantly, what innocent looking data will cause these methods to fail silently - in other words, give results that look reasonable, but are completely wrong. In conclusion, this book is not the easiest to read. But it is one of the best resources available when you need to learn how to handle basic and not-so-basic problems in the field of NLA.

Fantastic book, with great insight
I can't speak to the entire book, as I've only made significant use of the section of matrix solvers. Having said that, his explanation of Krylov methods was the most clear and well organized I've ever seen. His book is the first I've seen that so nicely ties together all such methods. It's true that his book is probably not going to be enough if you are planning to focus on this as your research topic. But for those of us who simply need to apply the field to their research, it is the best book I've found, and he goes out of his way to be helpful to the practitioner, a rare thing in a math book. (For example, he has a wonderful flowchart in Chapter 6 providing a rough guideline for selecting a linear system solver based on the properties of one's problem.)