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Get Free Ebook Accuracy and Stability of Numerical Algorithms
Get Free Ebook Accuracy and Stability of Numerical Algorithms
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Accuracy and Stability of Numerical Algorithms
Get Free Ebook Accuracy and Stability of Numerical Algorithms
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Review
'This book is a monumental work on the analysis of rounding error and will serve as a new standard textbook on this subject, especially for linear computation.' S. Hitotumatu, Mathematical Reviews'...This definitive source on the accuracy and stability of numerical algorithms is quite a bargain and a worthwhile addition to the library of any statistician heavily involved in computing.' Robert L. Strawderman, Journal of the American Statistical Association'...A monumental book that should be on the bookshelf of anyone engaged in numerics, be it as a specialist or as a user.' A. van der Sluis, ITW Nieuws'This text may become the new 'Bible' about accuracy and stability for the solution of systems of linear equations. It covers 688 pages carefully collected, investigated, and written ... One will find that this book is a very suitable and comprehensive reference for research in numerical linear algebra, software usage and development, and for numerical linear algebra courses.' N. Köckler, Zentrallblatt für Mathematik'... Nick Higham has assembled an enormous amount of important and useful material in a coherent, readable form. His book belongs on the shelf of anyone who has more than a casual interest in rounding error and matrix computations. I hope the author will give us the 600-odd page sequel. But if not, he has more than earned his respite - and our gratitude.' G. W. Stewart, SIAM Review
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Book Description
This book provides a thorough, up-to-date treatment of the behaviour of numerical algorithms in finite precision arithmetic. The coverage of the first edition has been expanded and updated, including numerous improvements to the original material. Its thorough indexes and extensive, up-to-date bibliography are in a readily accessible form.
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Product details
Hardcover: 710 pages
Publisher: SIAM: Society for Industrial and Applied Mathematics; 2 edition (August 1, 2002)
Language: English
ISBN-10: 0898715210
ISBN-13: 978-0898715217
Product Dimensions:
6 x 1.5 x 9 inches
Shipping Weight: 3 pounds (View shipping rates and policies)
Average Customer Review:
3.9 out of 5 stars
4 customer reviews
Amazon Best Sellers Rank:
#500,634 in Books (See Top 100 in Books)
I am amazed that I hadn't come across this book earlier. I was searching the internet for a particular algorithm and came across the pdf version of this book. I downloaded that (for free) and it answered my question. I then started reading other sections from the pdf and realised that I needed a paper copy because there was so much meat in there. So I bought a paper copy and have not regretted it at all.The explanations are thorough without losing clarity. I would recommend that anyone using numerical algorithms on a computer with IEEE floating point (i.e., everyone) have a copy to hand.
Higham does a pretty good job of explaining a difficult topic. It's been very helpful overall, but sometimes key equations and derivations are a bit difficult to find. He also doesn't (and probably can't) cover every possible floating point computation - so sometimes you have to find an operation that is similar to one you're working on, pay extremely close attention to his logic and derivation, then use it as a starting point for your own analysis/derivations.
The book was not in good conditions
This is an incredibly useful book for anyone who does a significant amount of programming with floating-point math and cares about its accuracy. There's this idea that floating point is not only imprecise -- which it is -- but also inherently opaque and unreliable, which it is NOT. This book will show you how to determine guaranteed, dependable bounds on the precision of your algorithms, and how to keep those bounds as tight as possible.The early chapters build up a set of tools for analyzing and bounding error. Rather than settle on a single method of analysis, the book provides an array of them, ranging from the simple and conservative to the elaborate and exact. Later chapters focus on specific algorithms and use cases, mostly in the context of linear algebra; it assumes basic knowledge of most of these algorithms. This would not be a good book for learning about LU decomposition. But it is a great book for learning how to depend on LU decomposition.It's dense in places, and has an unfortunate historical bent at times. Much ink is spent on the vagaries of the Cray FPU and the HP-48 calculator. Chapter 2, in particular, would have been considerably more readable if the author had stuck to base-2 representations, rather than complicating the math to encompass the rare and ultimately inconsequential base-10 and base-16 systems out there. There's also a certain amount of spaghetti writing... some of the material in the earlier chapters uses results from later chapters, which is particularly unfortunate in a book that's trying to build up a foundation of analysis methods in an ordered manner.But that is a tiny, tiny complaint, in the context of a book which has successfully taken such a complex, scary subject and made it truly approachable for the practical programmer. And given the fundamentally dry nature of the topic, the book is remarkably engaging. One could even call it a FUN READ. Arm yourself with a pad of paper and a compiler: you'll want to take frequent breaks to confirm the sometimes surprising revelations for yourself.
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