Customer Reviews

Applied Numerical Linear Algebra

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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.

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.)

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.

The book is somewhat clear and condense version of numerical method: linear algebra.
It seems that the book is quiet decent, but it is very difficult. Since I am not a numerical method guy, I found this book was very difficult to read if you don't have strong background of linear algebra and some basic numerical method knowledge. However, overall, the book was well-written and is good for ones who has good background of linear algebra. We used this book for CS class (I am not a CS student)...and it was okay.

I have been using this textbook for my Numerical Linear Algebra class, and it have been a great help, actually is a good complement to Numerical Linear Algebra by Lloyd N. Trefethen and David Bau III. I totally recommend it.

Clearest book on the subject. Great writing style. Used at the UofC for Financial Mathematics.

This book is really just an introduction to NLA and intended for the novice although it assumes some LA background. It is not necessary to read this if you plan PhD studies in the field since the book is only an introduction to the material and is honestly too simple. Read anything by Bjorck or Van Loan if you are a serious PhD student and want to do research in the field of NLA. This book is written for students that really don't plan research in the field of NLA but rather may need some skill level in NLA to perform their job or their own own research which may have some NLA exposure.