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Numerical Linear Algebra Paperback – June 1, 1997

ISBN-13: 978-0898713619 ISBN-10: 0898713617

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Numerical Linear Algebra + Matrix Computations (Johns Hopkins Studies in the Mathematical Sciences) + Applied Numerical Linear Algebra
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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: 10.1 x 7 x 0.8 inches
  • Shipping Weight: 1.4 pounds (View shipping rates and policies)
  • Average Customer Review: 4.2 out of 5 stars  See all reviews (20 customer reviews)
  • Amazon Best Sellers Rank: #30,370 in Books (See Top 100 in Books)

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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Customer Reviews

The book is very well written, and explains the concepts very carefully.
F. Cueto
This book should be required reading for anyone interested in computational numerics, especially those who are starting in the field.
Tia
Without that, you will need to be a math genius to find this book easy to read.
Xiao Hu

Most Helpful Customer Reviews

49 of 54 people found the following review helpful By Tia on February 24, 1999
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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24 of 25 people found the following review helpful By calvinnme HALL OF FAMETOP 1000 REVIEWERVINE VOICE on May 13, 2005
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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12 of 12 people found the following review helpful By Hart Wilson on June 24, 2002
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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7 of 7 people found the following review helpful By Chicago girl on July 24, 2006
Format: Paperback
I used this book at NYU in a graduate class on numerical linear algebra and it was great. The book is incredibly clear, starts from the basics and just goes from there. You won't be lost or feel like it has too little (and I usually have one of those two feelings about a math textbook).

The book is focused around matrix decompositions and does quite a bit of theoretical matrix algebra before it gets into accurate computation of decompositions, what this means and how various algorithms achieve it.

The theorems are clear and the proofs concise and easy to read.
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7 of 8 people found the following review helpful By Xiao Hu on August 30, 2010
Format: Paperback Verified Purchase
I am reviewing the book by Trefethen not by Demmel. There has been some confusion about these two books.

Many people commented that this book is logic and easy to read. Compared with some other books, this is true. However, the perquisite for this book is a sound understanding of linear algebra. Without that, you will need to be a math genius to find this book easy to read. So, this is an excellent book for your (at least my) first exposure to numerical linear algebra. It picks up about 40 important topics and cover them in such details that are not too overwhelming.

With the above positive side, I wish the author could expand the book and cover more topics or some topics in greater details. This book is good for an one semester course (Note that it has only just more than 300 pages for the main content). Many books are easily enough for two courses if not more. So, as a text book, this is excellent. But as a reference, you will need another book to go with it. Unfortunately, other books are not so easy to read.

By the way, for CG method the book is not excellent. You will need the article by Jonathan Richard Shewchuk. You can find it online. This is the best for CG.
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12 of 15 people found the following review helpful By Eric Boyer on October 9, 2010
Format: Paperback Verified Purchase
This is a fairly good, concise analysis of numerical linear algebra. It covers topics in a logical manner and overall has fairly good explanations. However, I feel that it has a few notable shortcomings.

Although explanations are fairly good, I found that they were too short. A minimum amount of detail is given, and there are very few examples. Also, there are very few end-of-chapter problems, and the ones given are almost all quite difficult and there are no answers available.

For these reasons I would only recommend this book for people with a strong background in linear algebra. I was an engineering undergraduate with a limited knowledge of linear algebra when I read it, but an upper-year math major or a math graduate would probably find this book to be ok, as long as their course instructor gives many supplementary resources, such as practice problems.
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3 of 3 people found the following review helpful By K. Long on June 4, 2013
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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