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Matrix Computations [Paperback]

Gene H. Golub , Charles F. Van Loan
4.5 out of 5 stars  See all reviews (13 customer reviews)
Price: CDN$ 57.50 & FREE Shipping. Details
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Book Description

Oct. 15 1996 0801854148 978-0801854149 3

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.

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'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'

About the Author

Gene H. Golub is professor of computer science at Stanford University. Charles F. Van Loan is professor of computer science at Cornell University.

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The proper study of matrix computations begins with the study of the matrix-matrix multiplication problem. Read the first page
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Customer Reviews

4.5 out of 5 stars
4.5 out of 5 stars
Most helpful customer reviews
5.0 out of 5 stars Got Matrices? Aug. 1 2003
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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5.0 out of 5 stars Great Mathematical Text June 21 2001
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.
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3.0 out of 5 stars Still state of the art? March 26 2002
By A Customer
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.
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4.0 out of 5 stars Not an introductory text! Aug. 23 2001
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).
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4.0 out of 5 stars from theory to practice. Aug. 8 2002
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.
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5.0 out of 5 stars Excellent book! May 24 1998
Great book on the computational aspects of matrix computations. Has much more detail than NRiC for matrix computations -- of course, NRiC covers more topics. One the few places you can actually find out how to code SVD. A steal at $30. Highly recommended!
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By A Customer
I recently bought this book and am amazed at how detailed the information is presented. This a great book for anyone doing numerical analysis on the computer. The details on how to work around ill-conditioned matrices is great.
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