Applied Numerical Linear Algebra [Paperback]

James W. Demmel (Author)

Book Description

ISBN-10: 0898713897 | ISBN-13: 978-0898713893 | Publication Date: August 1, 1997 | Edition: 1

Designed for 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 recommending which algorithms to use in various practical situations. 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.

Editorial Reviews

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.

Book Description

Designed for first-year graduate students from engineering and science disciplines, this comprehensive textbook covers the solution of linear systems, least squares problems, eigenvalue problems, and the singular value decomposition. The author presents state-of-the-art techniques for these problems, including recommendations of which algorithms to use in a variety of practical situations.

See all Editorial Reviews

Product Details

• Paperback: 431 pages
• Publisher: SIAM; 1 edition (August 1, 1997)
• Language: English
• ISBN-10: 0898713897
• ISBN-13: 978-0898713893
• Product Dimensions: 10 x 6.8 x 0.8 inches
• Shipping Weight: 2 pounds (View shipping rates and policies)
• Average Customer Review: 4.6 out of 5 stars  See all reviews (7 customer reviews)
• Amazon Best Sellers Rank: #412,093 in Books (See Top 100 in Books)

Customer Reviews

Most Helpful Customer Reviews

19 of 19 people found the following review helpful:

5.0 out of 5 stars This book grows on you, February 11, 2003

By 

Dan (Minnesota, USA) - See all my reviews

This review is from: Applied Numerical Linear Algebra (Paperback)

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.

11 of 11 people found the following review helpful:

5.0 out of 5 stars Fantastic book, with great insight, September 5, 2006

By 

Jonathan Birge (Cambridge, MA) - See all my reviews
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This review is from: Applied Numerical Linear Algebra (Paperback)

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.)

5.0 out of 5 stars State of the art stuff, December 29, 2011

By 

William B Cousins - See all my reviews

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This review is from: Applied Numerical Linear Algebra (Paperback)

If you want to learn the in's and out's of solving systems of linear equations on computers, this book can help you. It's also got stuff on eigenvalue problems, least squares problems, and a whole lot more. The author, James Demmel, is a pretty big deal and presents a fairly comprehensive survey of issues related to solving linear systems numerically such as the effects of floating point arithmetic error and memory management (these issues, of course, are relevant for all areas of numerical analysis). Nice selection of exercises as well.