Customer Reviews

Fundamentals of Matrix Computations

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

 

 

This book is not that famous as the golub/van loan bible but it is more than competitive. Especially for undergraduate or even graduate students who want to become familiar with computational aspects of linear algebra the bible might be to compact; watkins gives one more help to understand the main ideas.

when i first saw this book, i was very excited. i would have rated it 5 stars at that time. It's a much easier read than Golub's "matrix computations" and Demmel's "Applied Numerical Linear Algebra".

but then I saw Trefethen and Bau's "Numerical Linear Algebra", and I was totally amazed by that book. By comparison, this book by Watkins can only be rated 4 stars. It just doesn't match up to Trefethen's book in terms of elegance, smoothness, intuitiveness, and more importantly, focusing on the essence instead of being buried in the details.

if you are really interested in the topic of matrix computation, I suggest you start with Trefethen's book, and use Golub's book as reference later on.

After looking at a few books on matrix computations I believe that that Fundamentals of Matrix Computations by David S. Watkins does the best job of balancing theory and practice. Being a self learner I found this book easy to read, provided enough practical advice to write high quality algorithms, and provided a good foundation for more advanced subjects. Be sure to at least read through all the exercises since they often cover new material not discussed in the main section. Its worth working through many of the exercises and enough information is provided in general to validate your solution. As a self learner I'm often frustrated with some books that provided exercises but no way to know if you're right or not. I even went on to write a linear algebra library in Java which uses this book as the primary reference for a few of the algorithms, search for EJML if you are curious.

Golub and Van Loan's book covers much more material than Watkins but in a much more terse fashion. By terse I don't mean that Golub/Van Loan's is hard to understand, it is a very good book, but it is terse. I tend to use Golub/Van Loan's book more as a reference if I need to look something up quickly or if the material is not covered else where. There are also some situations important details are not mentioned in that book but are mentioned in Watkins' book. I have also looked though Numerical Linear Algebra by Trefethen and Bau. That book provided a good general high level overview of the basic subjects and in few cases was easier to understand, but I found it on the whole lacking in detail and often did not discuss important implementation issues.

(This review is for the 2nd Edition. I have yet to look at the 3rd.)

I used this book to learn iterative methods and absolutely loved it. The explanations are clear and the coverage of techniques is very comprehensive. The chapters on SVD (see cover illustration) and eigenvalue decomposition are also very well explained. I found it to be engaging and more approachable for a novice than Golub and van Loan (which by the way, you *should* read after reading Watkins :-))

Concepts are explained lucidly. The exercise problems are interesting. It would be a good idea to read this book first before moving on to books like the one by Golub/ Van Loan. Useful for self study...