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Fundamentals of Matrix Computations 2nd Edition

8 customer reviews
ISBN-13: 978-0471213949
ISBN-10: 0471213942
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Editorial Reviews

From the Publisher

The use of numerical methods continues to expand rapidly. At their heart lie matrix computations. Written in a clear, expository style, it allows students and professionals to build confidence in themselves by putting the theory behind matrix computations into practice instantly. Algorithms that allow students to work examples and write programs introduce each chapter. The book then moves on to discuss more complicated theoretical material. Using a step-by-step approach, it introduces mathematical material only as it is needed. Exercises range from routine computations and verifications to extensive programming projects and challenging proofs. --This text refers to an out of print or unavailable edition of this title.

From the Back Cover

A significantly revised and improved introduction to a critical aspect of scientific computation

Matrix computations lie at the heart of most scientific computational tasks. For any scientist or engineer doing large-scale simulations, an understanding of the topic is essential. Fundamentals of Matrix Computations, Second Edition explains matrix computations and the accompanying theory clearly and in detail, along with useful insights.

This Second Edition of a popular text has now been revised and improved to appeal to the needs of practicing scientists and graduate and advanced undergraduate students. New to this edition is the use of MATLAB for many of the exercises and examples, although the Fortran exercises in the First Edition have been kept for those who want to use them. This new edition includes:
* Numerous examples and exercises on applications including electrical circuits, elasticity (mass-spring systems), and simple partial differential equations
* Early introduction of the singular value decomposition
* A new chapter on iterative methods, including the powerful preconditioned conjugate-gradient method for solving symmetric, positive definite systems
* An introduction to new methods for solving large, sparse eigenvalue problems including the popular implicitly-restarted Arnoldi and Jacobi-Davidson methods

With in-depth discussions of such other topics as modern componentwise error analysis, reorthogonalization, and rank-one updates of the QR decomposition, Fundamentals of Matrix Computations, Second Edition will prove to be a versatile companion to novice and practicing mathematicians who seek mastery of matrix computation.

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Product Details

  • Hardcover: 640 pages
  • Publisher: Wiley-Interscience; 2 edition (May 24, 2002)
  • Language: English
  • ISBN-10: 0471213942
  • ISBN-13: 978-0471213949
  • Product Dimensions: 6.5 x 1.8 x 9.1 inches
  • Shipping Weight: 2.5 pounds (View shipping rates and policies)
  • Average Customer Review: 4.8 out of 5 stars  See all reviews (8 customer reviews)
  • Amazon Best Sellers Rank: #2,103,305 in Books (See Top 100 in Books)

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Most Helpful Customer Reviews

30 of 34 people found the following review helpful By Roger on November 14, 2003
Format: Hardcover
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.
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19 of 21 people found the following review helpful By A Customer on September 2, 2000
Format: Hardcover
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.
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9 of 9 people found the following review helpful By P. Abeles on October 20, 2010
Format: Hardcover Verified Purchase
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.)
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3 of 3 people found the following review helpful By RS on April 18, 2009
Format: Hardcover
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 :-))
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