An Introduction to Numerical Analysis [Paperback]

Kendall Atkinson (Author)

Book Description

ISBN-10: 0471624896 | ISBN-13: 978-0471624899 | Publication Date: January 17, 1989 | Edition: 2

This Second Edition of a standard numerical analysis text retains organization of the original edition, but all sections have been revised, some extensively, and bibliographies have been updated. New topics covered include optimization, trigonometric interpolation and the fast Fourier transform, numerical differentiation, the method of lines, boundary value problems, the conjugate gradient method, and the least squares solutions of systems of linear equations. Contains many problems, some with solutions.

Product Details

• Paperback: 712 pages
• Publisher: Wiley; 2 edition (January 17, 1989)
• Language: English
• ISBN-10: 0471624896
• ISBN-13: 978-0471624899
• Product Dimensions: 9.2 x 6.1 x 1.7 inches
• Shipping Weight: 2.2 pounds (View shipping rates and policies)
• Average Customer Review: 4.3 out of 5 stars  See all reviews (6 customer reviews)
• Amazon Best Sellers Rank: #560,187 in Books (See Top 100 in Books)

More About the Author

Discover books, learn about writers, read author blogs, and more.

Customer Reviews

Most Helpful Customer Reviews

10 of 10 people found the following review helpful:

5.0 out of 5 stars Excellent Book - not for everyone., July 2, 2004

By 

"[e-mail]" (Alexandria, VA United States) - See all my reviews

This review is from: An Introduction to Numerical Analysis (Paperback)

One of the best numerical analysis books I ever came across. This describes the theory behind numerical analysis, so if you expect to find a lot of numerical examples and written algorithms, this is NOT the book you're looking for.
Though there are some examples and algorithm, this is a math book, not a computer science oriented book. So buy this book if you are interested in the mathematical theory and ideas behind numerical analysis. Algorithms come and go, but the theory is always the same.
In my work as a computational physicist I use this book extensively and find it invaluable.
It takes some time to get used to, but little effort in understanding math never killed anyone.

7 of 7 people found the following review helpful:

5.0 out of 5 stars Knowledge that more people need, July 13, 2006

By 

wiredweird "wiredweird" (Earth, or somewhere nearby) - See all my reviews
(HALL OF FAME REVIEWER)    (TOP 500 REVIEWER)   

This review is from: An Introduction to Numerical Analysis (Paperback)

Numerical analysis is the study and art of determining how to get high quality answers out of computers with finite precision: in other words, all of them. This may not sound like a big issue - you can always use double precision, right? Well, no. Binary computers can't even represent 0.1 exactly. The numbers are wrong from the start, and go downhill fast. This book addresses the twin questions: how fast, and how to preserve as much accuracy as possible.

Atkinson gives a clear, readable exposition. Chapters cover all the classic topics: error analysis, solutions of nonlinear systems, and issues in vector and matrix manipulations. Matrix analysis skips discussion of sparse systems, though, and omits the different kinds of decompositions available for matrices in special form. He also presents chapters on integration and solution of differential equations, also staples of scientific computing, though maybe not quite as common as the other topics. Some of the best material, though, comes in sections on interpolation and function approximation, something that came up in my own work recently. A typical engineer equates polynomial approximation with truncated Taylor series, but that's a real mistake. Atkinson describes techniques based on sets of orthogonal polynomials. For an approximation of given polynomial degree, my application showed an order of magnitude reduction in error when we stopped using Taylor series. Your milage may vary, but orthogonal polynomials never give worse results. Also note that they don't affect how the approximation polynomial is used - just the way you pick the coefficients.

I fault this book only for minor points. First, discussion early on predates general acceptance of IEEE 754 - with denorms and other weirdness, problems are slightly different than before, but wide availability means that almost everyone has the same problems (early Java implementations notwithstanding). Second, it refers to "stable" problems as "well posed." Many problems, molecular dynamics among them, have inherently chaotic features no matter how they're phrased. The problem is what it is, and calling it "badly posed" suggest that beating it into shape will somehow "pose" it better - directing attention away from dealing with its true nature. Despite a few pickable nits, this is an outstanding introduction for a diligent reader, and should be on the shelves of any programmer involved in scientific computing.

//wiredweird

12 of 14 people found the following review helpful:

5.0 out of 5 stars Excellent introduction to numerical analysis, June 7, 2000

By A Customer

This review is from: An Introduction to Numerical Analysis (Paperback)

Out of some 7 or 8 numerical analysis texts from which I have learned or taught, this is easily the best. Its organization is standard, its exposition is excellent, it is comprehensive in its coverage of introductory topics, it has a very good bibliography, and its problems are very good. It is a good introduction for graduate students; it is a little advanced for most undergraduates, though strong undergraduates would benefit from its use. No computer coding is supplied though coding from the book's explanations is straightforward.