Matrix Computations (Johns Hopkins Studies in the Mathematical Sciences) [Hardcover]

Professor Gene H. Golub (Author), Professor Charles F. Van Loan (Author)

Book Description

Publication Date: October 7, 1996 | Series: Johns Hopkins Studies in the Mathematical Sciences

Revised and updated, the third edition of Golub and Van Loan's classic text in computer science provides essential information about the mathematical background and algorithmic skills required for the production of numerical software. This new edition includes thoroughly revised chapters on matrix multiplication problems and parallel matrix computations, expanded treatment of CS decomposition, an updated overview of floating point arithmetic, a more accurate rendition of the modified Gram-Schmidt process, and new material devoted to GMRES, QMR, and other methods designed to handle the sparse unsymmetric linear system problem.

Editorial Reviews

Review

'Praise for previous editions:' "A wealth of material, some old and classical, some new and still subject to debate. It will be a valuable reference source for workers in numerical linear algebra as well as a challenge to students."--'SIAM Review' "In purely academic terms the reader with an interest in matrix computations will find this book to be a mine of insight and information, and a provocation to thought; the annotated bibliographies are helpful to those wishing to explore further. One could not ask for more, and the book should be considered a resounding success."--'Bulletin of the Institute of Mathematics and its Applications'

Review

"A wealth of material, some old and classical, some new and still subject to debate. It will be a valuable reference source for workers in numerical linear algebra as well as a challenge to students." -- SIAM Review, reviewing a previous edition or volume

"In purely academic terms the reader with an interest in matrix computations will find this book to be a mine of insight and information, and a provocation to thought; the annotated bibliographies are helpful to those wishing to explore further. One could not ask for more, and the book should be considered a resounding success." -- Bulletin of the Institute of Mathematics and its Applications, reviewing a previous edition or volume

"The authors have rewritten and clarified many of the proofs and derivations from the first edition. They have also added new topics such as Arnoldi iteration, domain decomposition methods, and hyperbolic downdating. Clearly the second edition is an invaluable reference book that should be in every university library. With the new proofs and derivations, it should remain the text of choice for graduate courses in matrix computations" -- Image: Bulletin of the International Linear Algebra Society, reviewing a previous edition or volume

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Product Details

• Hardcover: 728 pages
• Publisher: The Johns Hopkins University Press; 3rd edition (October 7, 1996)
• Language: English
• ISBN-10: 080185413X
• ISBN-13: 978-0801854132
• Product Dimensions: 9.8 x 6.5 x 1.8 inches
• Shipping Weight: 2.6 pounds
• Average Customer Review: 4.4 out of 5 stars  See all reviews (32 customer reviews)
• Amazon Best Sellers Rank: #4,228,821 in Books (See Top 100 in Books)

Customer Reviews

Most Helpful Customer Reviews

83 of 87 people found the following review helpful:

3.0 out of 5 stars Just a simple remark, July 20, 2005

By 

Ali Civril (Troy, NY USA) - See all my reviews
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This review is from: Matrix Computations (Johns Hopkins Studies in Mathematical Sciences)(3rd Edition) (Paperback)

This is not a complete review. I just wanted to say something important about the book. I'm a second year computer science PhD student, comfortable with linear algebra. I have been using this book for a couple of months to implement SVD (singular value decomposition) and unfortunately the book turned out to introduce some difficulties.

First of all, it's annoyingly terse! You must be quite comfortable with matrices and all the manipulations etc. to "grasp" the main idea behind an algorithm. I'm talking about truly understanding, not implementing line by line. Most of the times, you will need a paper and pencil to understand what's going on during the execution of an algorithm.

Yet, there's one more important thing: There are typos, and worse: there are mistakes. A specific example:

page 456, Algorithm 8.6.2 The SVD Algorithm

It doesn't talk about how to extract U and V in the decomposition A = U^T*D*V and the last line is incorrect.

diag(I_p, U, I_{q+m-n}) is not an n*n matrix, so you cannot multiply B with this matrix from left. Maybe, there's something I couldn't catch, but this is book's deficiency again.

page 252 Example 5.4.2 about Householder Bidiagonalization

The given matrices do not constitute a correct bidiagonalization, I checked them with Matlab.

and a typo: page 216 5.1.9 Applying Givens rotations, the 4th and 5th line of the algorithm is incorrectly written.

A(1, j) = ...

A(2, j) = ...

should be

A(i, j) = ...

A(k, j) = ...

So, these are the ones I encountered. This book is unmatched in its category in terms of depth and coverage, but it definitely needs a new edition with a more careful treatment.

30 of 31 people found the following review helpful:

5.0 out of 5 stars Got Matrices?, August 1, 2003

By 

James Arvo (Pasadena, CA USA) - See all my reviews
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This review is from: Matrix Computations (Johns Hopkins Studies in Mathematical Sciences)(3rd Edition) (Paperback)

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.

23 of 24 people found the following review helpful:

5.0 out of 5 stars The standard reference, August 18, 2006

By 

wiredweird "wiredweird" (Earth, or somewhere nearby) - See all my reviews
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This review is from: Matrix Computations (Johns Hopkins Studies in the Mathematical Sciences) (Paperback)

First, this isn't Numerical Recipes. If you're looking for cut&paste code, you're just looking in the wrong place. This is for people who need a deep understanding of the computational issues, and are going to put a lot of time into an implementation. It's for people who are completely at ease with linear algebra, standard matrix-oriented problems, and dense mathematical notation.

Despite its demand for a reader well versed in theory, this really is about practice. It's about the nasty effects of finite-precision arithmetic, about specific ways of minimizing the harm they cause. These techniques take full advantage of any special features in the problem, including banding and symmetry. This also deals briefly with caching issues, which are even more important now than when this book was written. Cache data can get to the processor in 1-10 cycles, in a modern workstation processor, but main memory access costs 100-1000 cycles. TLB misses can cost many thousands of cycles, even when data is already in memory. Clearly, good data structures and well-orgnized access patterns can make a huge difference, but one that is mentioned only briefly. The section on parallel computation is brief and helpful, but overdue for review. The authors could never have foreseen today's multi-(thread, core, processor) systems, Blue Gene, or clusters.

Still, this is an indispensable reference for someone in the thick of numerical computation. Most programmers would do better, in lots of ways, usingn the GNU Scientific Library or one of the other production-quality packages out there. They don't always do the job, though. Emerging architectures, include hardware threading and reconfigurable computing, need new implementations of even well-known algorithms. If you have big mathematical problems and machines too exotic for the standard tools, you're on your own. Numerical computing is such a large topic that no one book can possibly cover it all. In the end, though, many other problems reduce to linear systems, and that's where this comes in. It may not be theonly book you'll need, but you'll need it.

//wiredweird