Customer Reviews

Matrix Computations

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

 

 

My course was suffering before I bought this book. I found it contains every algorithm, and why we use it,but also how we store the data. A great author,a great book

This is the book I turn to first when I have to deal with a problem in numerical linear algebra, it's clearly written and has extensive references.

This is one of the definitive texts on computational linear algebra, or more specifically, on matrix computations. The term "matrix computations" is actually the more apt name because the book focuses on computational issues involving matrices,the currency of linear algebra, rather than on linear algebra in the abstract. As an example of this distinction, the authors develop both "saxpy" (scalar "a" times vector "x" plus vector "y") based algorithms and "gaxpy" (generalized saxpy, where "a" is a matrix) based algorithms, which are organized to exploit very efficient low-level matrix computations. This is an important organizing concept that can lead to more efficient matrix algorithms.

For each important algorithm discussed, the authors provide a concise and rigorous mathematical development followed by crystal clear pseudo-code. The pseudo-code has a Pascal-like syntax, but with embedded Matlab abbreviations that make common low-level matrix operations extremely easy to express. The authors also use indentation rather than tedious BEGIN-END notation, another convention that makes the pseudo-code crisp and easy to understand. I have found it quite easy to code up various algorithms from the pseudo-code descriptions given in this book. The authors cover most of the traditional topics such as Gaussian elimination, matrix factorizations (LU, QR, and SVD), eigenvalue problems (symmetric and unsymmetric), iterative methods, Lanczos method, othogonalization and least squares (both constrained and unconstrained), as well as basic linear algebra and error analysis.

I've use this book extensively during the past ten years. It's an invaluable resource for teaching numerical analysis (which invariably includes matrix computations), and for virtually any research that involves computational linear algebra. If you've got matrices, chances are you will appreciate having this book around.

A few years ago this book permitted me to go reliably from
theoretical linear algebra to practical large-scale numerical
computations, using also LAPACK. I think this is its place:
from the university course level to the practical side.
On the other hand, one cannot really say it is as readable
as, say, Numerical Recipes: it has a quite terse style.

It is now 6 years ago when the last version of this once
superb book was released. Meanwhile, bunches of books
aiming a similiar audience were published. Some of them,
in particular G.W. Stewarts, are nowadays more seasonable.
Notably, the "iterative" sections ask for light
refreshments. The lack of references to appropriate
software routines in these parts is another disadvantage
which could be easily overcome in a new edition.

Once you have a grounding in matrix analysis and linear algebra this book makes a good reference. His explanations tend to be terse (even exceptionally so)- more suited for reminding someone who already knows how the algorithm works or was derived and simply can't remember the details. It lost a star as I've found some annoying typos (for example, in the pseudocode for the GMRES algorithm).

This book should be placed alongside "Principles of Mathematical Analysis" by Walter Rudin and "Finite Dimensional Vector Spaces" by Paul Halmos as a classic text, one which students/professionals of mathematics will use for years to come. A solid book covering computational matrix theory. I myself used it as a tool to bridge the gap between my formal training in Mathematics and my serious interest in computers. Reader should have some knowledge of basic linear algebra(ie understanding of vector spaces, L2 norms, etc..) before attempting this book. Excercises could be better. A good purchase for those with a more than passing interest.

When I need to solve a large system of linear equations or better understand an algorithm I am using, this book has proven to be the best place to go. It is broad in scope and the writing is clear.

The book is good, but it could have more useful examples and a less complicated text.

Presents an extremely thorough and clear study of one of the most important branches of Applied Mathematics