Matrix Computations (Johns Hopkins Series in the Mathematical Sciences)
Author: Gene H. Golub, Charles F. Van Loan
List Price: $45.95
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ISBN: 0801854148
Publisher: Johns Hopkins Univ Pr (November, 1996)
Sales Rank: 21,944
Average Customer Rating: 4.23 out of 5
Customer Reviews
Rating: 5 out of 5
One of the best books on the subject
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.
Rating: 4 out of 5
Not an introductory text!
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).
Rating: 5 out of 5
Got Matrices?
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.
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