Matrix Computations (Johns Hopkins Studies in Mathematical Sciences)(3rd Edition)

Book Description

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.

Customer Reviews:

Matrix Computations is an excellent guide to understanding and implementing Numerical Linear Algebra.......2007-09-30

This book is an excellent book for the student or researcher who needs to understand clearly the issues that arise in the developement of algorithms for the solution and analysis of linear systems. It gives a great explanation of how one operation like solving a linear system or doing just forward or backward solves can be mapped to basic BLAS primitives and how these variations have been implemented in popular libraries such as Lapack or BLAS and the archetectual reasons why one approach may be more optimized than another, row versus column operations, for example.

For the student it provides a nice walk through on the develpment of these algorithms and for the researcher provides a life long resource for reference to the many algorithms that are laid out here.

This book is clear and easy to follow and it is recomended for anyone who is serious about learning how to design and implement efficient linear algebra algorithms for a variety of archetectual and coding language environments.

bible.......2007-09-24

This book is a bible in matrix computation. While they have a lot of details on everything, though, the notations are rather complicated and hard-to-follow.

Gargantuan Copy and Paste Monument.......2007-05-07

Three stars are for:

(1) Relatively cheap price.
(2) Comprehensive but shallow coverage.
(3) Mass availability.

Hypothesis: The only three prematurely worn keys in Golub & Van Loan's keyboards must be: Control, C and V, since these form the shortcut for copy and paste operations.

There is no depth in this book when compared to classic matrix theory books, although I understand that this may distract from the possible use of the book as a reference manual. But as written, it is of little value in addition to Numerical Recipes; the latter has at least decent text this one does not have character, too much copying and pasting eliminated the book to form a skeleton.

What are the basis books for comparison?

1. Wilkinson, Algebraic Eigenvalue Problem. Super but expensive (>$100).
2. Marcus & Minc, A survey of Matrix Theory and Matrix Inequalities. Super but inexpensive (10$).
3. Horn and Johnson, Matrix Analysis, comprehensive, pretty good, and similarly priced to this ($30).

I am not suggesting that the content should mirror these books but the quality and depth should but despite being in its third edition, the book is full of errors both in pseudo-code and text.

The CTRL-C/CTRL-V effort is so insane that authors' could not help themselves to copy Wilkinson's theorem presentation sequence about the symmetric eigenvalue problem, but Wilkinson's commentary from his book (see Hoffman-Wielandt theorem in Golub & VanLoan second edition).

Whenever someone tells me that they learned something from Golub and Van Loan, I can not help myself to question what they thought they might have learned.

In almost all cases, Golub and Van Loan fans appear to know of a result through memorization without any clue about how it is derived and why it is important. So if this is your bible, then probably you do not deserve a job that requires critical thinking.

The books popularity tells something about the state of the academia: for example, the hotshots of signal processing republished Golub and Van Loan a few times to get their IEEE Fellow titles. Google for 'Multistage Wiener Filter', 'Relationship Conjugate Gradient MSWNF', 'Procrustes Rotations ESPRIT'. Definitely a field that does not appreciate critical thinking but fast copy and paste effort through graduate student slavery.

Exactly what I needed.......2007-03-08

I have been using "canned" programs for matrix calculations, but I needed to learn how they actaully work. This book provided exactly the information that I needed. This book is not for beginners--it requires a pretty good knowledge of linear algebra, but if you have that, this book will be most helpful in understanding sophisticated computational methods

The bible of numerical linear algebra.......2007-01-01

This book is the standard reference for all numerical linear algebra. It is a graduate-level applied math textbook written by practicing professionals for practicing professionals. If you are new to the topic you would probably prefer something like James Demmel's Applied Numerical Linear Algebra.

If you are interested in implementing the algorithms in this book, stop right now and first make sure that you can't use MATLAB or LAPACK instead, or even ScaLAPACK if you need a parallel implementation. Getting these algorithms right is hard, and the hard work has probably already been done by somebody else. LAPACK contains the accumulated wisdom of over forty years of research in numerical linear algebra, and MATLAB contains LAPACK. Don't re-invent the wheel.

On the other hand, if you want to understand how LAPACK works, or if you need to understand its numerical accuracy and stability, then this is the book for you.

Another reviewer has mentioned that this book contains numerous errata in the formulas. This is still true as of the third edition. Usually it is possible to detect and correct these errors by reading and understanding the surrounding text, but beware.

Average customer rating:

good, but not the best
interesting alternative to golub/van loan

Fundamentals of Matrix Computations
David S. Watkins
Manufacturer: Wiley-Interscience
ProductGroup: Book
Binding: Hardcover

General | Science | Subjects | Books

General | Mathematics | Science | Subjects | Books

Matrices | Mathematics | Science | Subjects | Books

Look Inside Science Books | Trip | Specialty Stores | Books

All Titles | Qualifying Textbooks - Fall 2007 | Stores | Books

Professional | Qualifying Textbooks - Fall 2007 | Stores | Books

Science | Qualifying Textbooks - Fall 2007 | Stores | Books
Similar Items:

ASIN: 0471213942

Book Description

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.

Download Description

Customer Reviews:

good, but not the best.......2003-11-15

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.

interesting alternative to golub/van loan.......2000-09-03

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.

Matrix iterative analysis (Prentice-Hall series in automatic computation)

Average customer rating:

Excellent, but very dated

Matrix iterative analysis (Prentice-Hall series in automatic computation)
Richard S Varga
Manufacturer: Prentice-Hall
ProductGroup: Book
Binding: Unknown Binding

ASIN: B0006AY57S

Book Description

This book is a revised version of the first edition, originally published by Prentice Hall in 1962 and regarded as a classic in its field. In some places, newer research results, e.g. results on weak regular splittings, have been incorported in the revision, and in other places, new material has been added in the chapters, as well as at the end of chapters, in the form of additional up-to-date references and some recent theorems to give the reader some newer directions to pursue. The material in the new chapters is basically self-contained and more exercises have been provided for the readers. While the original version was more linear algebra oriented, the revision attempts to emphasize tools from other areas, such as approximation theory and conformal mapping theory, to access newer results of interest. The book should be of great interest to researchers and graduate students in the field of numerical analysis.

Customer Reviews:

Excellent, but very dated.......2001-06-03

The Editorial Review on Amazon's site says: "While the original version was more linear algebra oriented, the revision attempts to emphasize tools from other areas, such as approximation theory and conformal mapping theory, to access newer results of interest". These remarks give an incorrect flavor for the book. Of approximately 350 references, less than a dozen are post 1990. The vast majority are from 1950 to 1965. The author repeatedly refers to "more recent" results with references to the early 1960's. So much for "newer results". The author's remarks in the preface to the new edition are much more informative: "...just what could easily be added [to the new edition]. For example, even a modest treatment of finite elements...was questionable. This was also the case for multigrid methods, Krylov subspace methods, preconditioning methods, and incomplete factorization methods. In the end, only a few items were added... These items include ovals of Cassini, a semi-iterative analysis of SOR methods,.... and matrix rational approximations to exp(-z)."

You will notice that "conformal mapping" didn't make the grade as a centerpiece of the new edition, and neither is it mentioned in the Table of Contents, nor the Index.

Book Description

Numerical linear algebra is far too broad a subject to treat in a single introductory volume. Stewart has chosen to treat algorithms for solving linear systems, linear least squares problems, and eigenvalue problems involving matrices whose elements can all be contained in the high-speed storage of a computer. By way of theory, the author has chosen to discuss the theory of norms and perturbation theory for linear systems and for the algebraic eigenvalue problem. These choices exclude, among other things, the solution of large sparse linear systems by direct and iterative methods, linear programming, and the useful Perron-Frobenious theory and its extensions. However, a person who has fully mastered the material in this book should be well prepared for independent study in other areas of numerical linear algebra.

Parallel Algorithms for Matrix Computations

Average customer rating:

Parallel Algorithms for Matrix Computations
K. A. Gallivan , Michael T. Heath , Esmond Ng , James M. Ortega , Barry W. Peyton , R. J. Plemmons , Charles H. Romine , A. H. Sameh , and Robert G. Voigt
Manufacturer: Society for Industrial Mathematics
ProductGroup: Book
Binding: Paperback

Parallel Processing Computers | Hardware | Computers & Internet | Subjects | Books

General | Programming | Computers & Internet | Subjects | Books

General | Computers & Internet | Subjects | Books

General | Science | Subjects | Books

General | Mathematics | Science | Subjects | Books

Matrices | Mathematics | Science | Subjects | Books

All Titles | Qualifying Textbooks - Fall 2007 | Stores | Books
ASIN: 0898712602

Book Description

Describes a selection of important parallel algorithms for matrix computations. Reviews the current status and provides an overall perspective of parallel algorithms for solving problems arising in the major areas of numerical linear algebra, including (1) direct solution of dense, structured, or sparse linear systems, (2) dense or structured least squares computations, (3) dense or structured eigenvaluen and singular value computations, and (4) rapid elliptic solvers. The book emphasizes computational primitives whose efficient execution on parallel and vector computers is essential to obtain high performance algorithms.

Book Description

This volume in matrix structural analysis is written for senior undergraduate students. Matrix structural analysis is presented in the various chapters for structures modeled as beams, plane frames, grid frames, space frames, plane trusses, and space trusses. An introduction to the related topic of the finite element method is also given. A CD-ROM accompanying this book contains not only the student version of SAP 2000 but also user manuals and numerous sample problems and examples. Throughout the book, illustrative examples are given with detailed solutions derived from hand calculations and from using the computer program. Long mathematical proofs have been relegated to a section on analytical problems at the end of each chapter. Appendices give the equivalent end forces for typical loading needed in matrix structural analysis. An extensive glossary is also included; this serves as a convenient reference for the student to locate definitions, concepts, and formulae. This text is essential for undergraduate civil engineering students. Professional civil engineers interested in a simple presentation of matrix structural analysis will also find the book useful.

Parallel Algorithms and Matrix Computation (Oxford Applied Mathematics and Computing Science Series)

Average customer rating:

Parallel Algorithms and Matrix Computation (Oxford Applied Mathematics and Computing Science Series)
Jagdish J. Modi
Manufacturer: Oxford University Press, USA
ProductGroup: Book
Binding: Hardcover

Parallel Processing Computers | Hardware | Computers & Internet | Subjects | Books

General | Computers & Internet | Subjects | Books

Look Inside Computer Books | Trip | Specialty Stores | Books
ASIN: 0198596553

Book Description

One of the first textbooks on the topic, this book brings together and further articulates the fundamental concepts in parallel computing. It covers the application of parallel algorithms to numerical linear algebra, with an emphasis on the design and analysis of algorithms that are of
particular importance in both industrial and academic research. The first part is devoted to a discussion of the general principles and techniques involved, and is illustrated by numerous examples. Dr. Modi goes on to describe some key areas of application, such as sorting, linear systems, partial
differential equations, singular-value decomposition, and eigenvalue analysis. Based on a lecture course at the University of Cambridge, the text will appeal to those with an interest in the design and implementations of algorithms in parallel computing.

Average customer rating:

Solid Book, but VERY Theoretical

Matrix Algorithms
G. W. Stewart
Manufacturer: SIAM: Society for Industrial and Applied Mathematics
ProductGroup: Book
Binding: Paperback

General | Software | Computers & Internet | Subjects | Books

General | Science | Subjects | Books

Mathematical Analysis | Mathematics | Science | Subjects | Books

Matrices | Mathematics | Science | Subjects | Books

All Titles | Qualifying Textbooks - Fall 2007 | Stores | Books
Similar Items:

ASIN: 0898714141

Book Description

This thorough, concise, and superbly written volume is the first in a self-contained five-volume series devoted to matrix algorithms. It focuses on the computation of matrix decompositions - the factorization of matrices into products of similar ones. The first two chapters provide the required background from mathematics and computer science needed to work effectively in matrix computations. The remaining chapters are devoted to the computation and applications of the LU and QR decompositions. The series is aimed at the nonspecialist who needs more than black-box proficiency with matrix computations. A certain knowledge of elementary analysis and linear algebra is assumed, as well as a reasonable amount of programming experience. The guiding principle, that if something is worth explaining, it is worth explaining fully, has necessarily restricted the scope of the series, but the selection of topics should give the reader a sound basis for further study.

Customer Reviews:

Solid Book, but VERY Theoretical.......2005-07-12

Please be warned that this book is heavily designed toward matrix theory, rather than the algorithm itself. Therefore, if you are math-averse, you'd better look for other books that offers much lighter theory such as Numerical Recipes. However, if you are not deterred by Greek letters or complicated formulas and eager to learn the theories behind all of the algorithms, this book is for you. Although the author claims that the intended audience is "nonspecialist", I find that this book is most suitable to scientists or grad students, rather than common programmers.

The author explicitly assumes that you know some programming and some linear algebra. Although chapter 1 explains basic matrix theories, you'll need to possess strong basic matrix knowledge -- such as matrix additions, substractions, transpositions, determinants, inverses -- as the author glosses over those on the very first few pages. Still on chapter 1, the author builds up the theories a lot, both matrix theory and linear algebra. He explains many terms such as rank, norms, decompositions, singularity, etc. He also give some proofs on some theorems. These advanced theories will be developed in corresponding later chapters.

Chapter 2 discusses keywords and notations used in the algorithm, such as "for", "if", etc. The pseudocode looks like Pascal. Here, he also give some samples of "easier" algorithms, such as forward substitution and inversion of triangular matrix. He also explains the classical Big O notation briefly and use the sample algorithms as examples on how to compute the Big O notation out. Then, followed by how matrices are stored in the memory and how to optimize the algorithm based on how we store the matrix in the memory. Then, he discuses, quite elaborately, on how to compute rounding error on algorithms and numerical stability of a given algorithm. This last section of chapter 2 is extremely important for those who demands accuracy. This numerical issues will be thoroughly discussed in the later chapters too.

Chapter 3 discusses Gaussian Elimination, LU Decomposition, Cholesky decompositions and their respective variants. The author explains all theory behind them, complete with proofs, discussion on accuracy / rounding error, and Big-O theoretical performance. The algorithms are presented in Pascal-like pseudocode, whose notation described in chapter 2. The author also discuss how certain variants are more beneficial than others (in terms of speed, numerical stability, etc), again, often complete with proofs (or left as an "exercise" for the reader). Theories from chapter 1 are also revisited and expanded as needed.

Chapter 4 discusses QR decomposition and its variants. Complete with background theory, proofs, discussion on accuracy, etc. Just like in chapter 3. It also discusses updating issues and how to adapt QR to linear solutions.

Chapter 5 discusses rank-reducing decompositions. Modifications of previous decompositions to suit this rank-reducing needs, QLP decompositions, and variants of UTV decompositions. Theories, proofs, and discussion of accuracies are all in, as usual.

Speaking of the theory, it's great. It's thorough and the proofs are there even when I think it's not that necessary. By studying this book, one will understand all the theory behind all the decompositions discussed. Numerical issues are discussed very thoroughly, which in itself justifies the price of this book.

However, my main qualms are:

1. Dearth of real examples
Many examples discussed in the book are way too abstract. Sometimes there are no examples at all. For example: There are no examples in doing Cholesky decomposition. The author only gives an example when the pivoting is necessary (and thus leads to small modification of the algorithm). What about the one that doesn't require any pivoting? Even with the one that requires pivoting, the examples are not given as step-by-step run through. The reader is assumed to know which several steps of the algorithms have already taken place from one matrix to another. In the case of Hessenberg matrix, there are no examples at all. This book is certainly not intended for "nonspecialists".

2. Way too much theory and proofs
I'm inclined to say that there are way too much theory than it is necessary. I'm not math-averse at all. I was hoping that this book is more practical as the author claims.

3. BLAS acronym
Maybe this one is a small annoyance. The author uses BLAS acronym a lot. Such as "xeuib" that stands for "X Equals U^(-1) times B". I'm not familiar with BLAS and I have to keep refering to Figure 2.2 to figure one out.

That being said, this is a solid book for explaining theories behind basic decomposition. Treatment on the programming and pragmatic side is rather lacking. Definitely not for the faint-hearted.

Handbook for Matrix Computations (Frontiers in Applied Mathematics)

Average customer rating:

Handbook for Matrix Computations (Frontiers in Applied Mathematics)
Charles Van Loan , and Thomas F. Coleman
Manufacturer: Society for Industrial Mathematics
ProductGroup: Book
Binding: Paperback

General | Computers & Internet | Subjects | Books

General | Mathematics | Science | Subjects | Books

Matrices | Mathematics | Science | Subjects | Books

Book Description

Provides the user with a step-by-step introduction to Fortran 77, BLAS, LINPACK, and MATLAB. It is a reference that spans several levels of practical matrix computations with a strong emphasis on examples and ‘hands on’ experience.

Black Box Classical Groups (Memoirs of the American Mathematical Society)

Average customer rating:

Black Box Classical Groups (Memoirs of the American Mathematical Society)
William M. Kantor , and Akos Seress
Manufacturer: American Mathematical Society
ProductGroup: Book
Binding: Paperback

General | Science | Subjects | Books

General | Mathematics | Science | Subjects | Books

Books:

Books Index

Books Home

Recommended Books