Customer Reviews

Numerical Linear Algebra

5 star:		(9)
4 star:		(3)
3 star:		(1)
2 star:		(1)
1 star:		(0)

 

 

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 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.

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.

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.

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.

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.

I am a second year PhD student in Operations Research and for long I had been looking for a book in linear algebra to help me learn it myself (as I see that I need it no matter what research I want to do. It's just a good tool to know). One of my friends recommended this book to me, I got it and I am very happy with it. The book is great in different ways:
-it is in the form of short lectures and for me who wants to learn linear algebra step by step, this is a perfect approach. You will have a 5-6 page lecture so whenever you start, you are set to finish that lecture.
-It gives you intuition and understanding about what is really happenning geometrically which is amazing. To me, it is very important to have the "feeling" of what is happening because it is only then that you can think about bringing your real problem in this framework.
-The examples in lectures clarify the subject while exercises give you a chance to learn even more.
If you are new to linear algebra or know it but want to refresh your mind on intuitions and systematic thinking, I highly recommend this book.

The book is very well written, and explains the concepts very carefully.

A very important characteristic is that the authors strive not only for rigor, but also for interpretation. Most topics are very well connected with a very clear style.

Excellent book on the subject. A must have.

The book is still in a very good condition. It was shipped very fast, and I got the book three days after class started. However, the book is really hard to understand. Well, most of time the linear algebra books are hard to understand..

The book arrive in time and is in perfect condition(just like its online description "Like New"). I've read chapters of this book and find that it is very suitable for reader who has a background of linear algebra but still not skillful enough to conquer the classic Matrix Computions.