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Numerical Linear Algebra

4.2 out of 5 stars 36 customer reviews
ISBN-13: 978-0898713619
ISBN-10: 0898713617
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  • Numerical Linear Algebra
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Editorial Reviews

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.

Book Description

This is a concise, insightful introduction to the field of numerical linear algebra. The authors' clear, inviting style and evident love of the field, along with their eloquent presentation of the most fundamental ideas in numerical linear algebra, make it popular with teachers and students alike.
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Product Details

  • Paperback: 373 pages
  • Publisher: SIAM: Society for Industrial and Applied Mathematics (June 1, 1997)
  • Language: English
  • ISBN-10: 0898713617
  • ISBN-13: 978-0898713619
  • Product Dimensions: 6 x 0.8 x 9 inches
  • Shipping Weight: 1.4 pounds (View shipping rates and policies)
  • Average Customer Review: 4.2 out of 5 stars  See all reviews (36 customer reviews)
  • Amazon Best Sellers Rank: #35,042 in Books (See Top 100 in Books)

Customer Reviews

Top Customer Reviews

Format: 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.
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Format: Paperback
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.
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Format: Paperback
This book on Linear Algebra is excellent. In particular chapters seven through thirty (as far as I have read) are great for self-directed study. However, I found chapters one through six ( through Projectors) a bit terse. Therefore I would highly recommend this book for self-study ONLY IF you already have a good idea of the concept of basic linear algebra including matrix norms, the singular value decomposition, and projectors, and also the correct way to perform a proof...and by a "good idea" I mean you already know how to use these ideas in a practical way. Otherwise, you should only use this book if you have a truly good instructor to guide you through the early material. I started out taking a class using this book four years ago from a poor instructor, and I and the entire class, as far as I could tell from casual conversation, were completely lost. I dropped the class and retook it just recently with an excellent instructor. Her help and insight made a world of difference. It will also help to have a copy of "Matrix Computations" by Golub and Van Loan for reference, especially when you get to the later chapters and eigenproblems.
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Format: 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.)
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Format: Hardcover
The chapters on numerical stability of algorithms and conditioning of numerical problems are excellent. While the focus is of course linear algebra, these principles can be readily extended to all computational mathematics. If you regularly use computational methods and have not yet studied elementary error analysis, this book may revolutionize how you perceive numerical problems.
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Format: Paperback Verified Purchase
Face it, most math textbooks are awful: boring to read, not much insight, little more than a compendium of definitions, theorems, proofs, and examples. Trefethen and Bau is an exception to that rule. Indeed, the field of numerical linear algebra is unusual in having available several top-notch textbooks: Golub and Van Loan, Stewart's two volumes, Saad's books on iterative methods, Demmel's introduction, Watkins' undergraduate level treatment, and T&B. All of these are excellent (and any student in numerical analysis should delve into all of them) but to my tastes T&B and Stewart are the standouts for insight and simply being fun to read.

If you're a student using T&B in a course, to use it effectively you need to understand that T&B is a book to be read carefully for understanding; it's not a typical textbook suited only for "mining" for examples and solutions to homework problems. My students have sometimes complained -- accurately -- that T&B is short on details and worked examples, and many of the proofs are just sketches. But that's a feature, not a bug: you can learn much by filling in the missing steps. This is book for reading, so take the time to read it, to think about what you've read, and to fill in the gaps; it's worth it. If you need some worked examples, Watkins has them in great detail and would be a good supplement to T&B (though see the caveat below).

The only minor gripe I have about T&B is that the order of topics (QR before LU before Cholesky) is unusual, which makes it a little awkward to coordinate with other books such as Watkins which do Cholesky before LU before QR.
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