- Paperback: 712 pages
- Publisher: Wiley; 2 edition (January 17, 1989)
- Language: English
- ISBN-10: 0471624896
- ISBN-13: 978-0471624899
- Product Dimensions: 6.4 x 1.2 x 9.6 inches
- Shipping Weight: 2.7 pounds (View shipping rates and policies)
- Average Customer Review: 7 customer reviews
- Amazon Best Sellers Rank: #908,923 in Books (See Top 100 in Books)
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An Introduction to Numerical Analysis 2nd Edition
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Otherwise a great book. Lots of material.
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.
One unfortunate distraction, that appears on every page, is the obsolete font. By comparison with fonts in more recently written texts, including those books by the same publisher, the printed text of this book appears smudged. Despite the author's claim in the preface to the second edition, it is not true that "all sections have been rewritten". But maths books are notoriously expensive to retype, because of the intricate equations that appear. I suspect what happened here is that the publisher largely went the easy route of re-using the older camera-ready files.
Another backwardness is the reference in the above mentioned preface, written in 1987, to software packages by IMSL and NAG. These certainly still exist. But by now, packages by Mathematica, Maple and Matlab are more prevalent, at least for undergraduate students. Though for readers experienced in this subject or in programming, they should be able to write code implementing the algorithms.
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.