17 of 17 people found the following review helpful:
4.0 out of 5 stars
Wide range of topics covered in detail, but lots of mistakes, May 9, 2000
I was quite amazed by the wide range of topics and applications covered by this book. And yet, each topic is covered in detail, with many algorithms presented to achieve a certain goal. The various algorithms are always summarised and compared, so that it is a simple matter to know which algorithm to choose depending on the circumstances of the problem at hand. I liked the very detailed examples which tend to run over a good number of iterations so that one can easily test one's understanding of the operation of the algorithm.
However, the disappointment lay in the number of mistakes that are made. Most of them are very subtle, and are only discovered if you go through the text carefully, or try to implement an algorithm based on the example pseudocode. In most cases it is the pseudocode that has gone wrong. If you are only a beginner programmer, then it will be difficult to sift through the poorly written pseudocode. On the other hand, a seasoned programmer will have no problems.
In summary - a top class book marred by some mistakes. If you know how to program, then this book is for you. Beginner programmers will be slowed somewhat by the poor pseudocode.
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7 of 7 people found the following review helpful:
3.0 out of 5 stars
Numerous errors hurt an otherwise decent book, October 31, 2005
This review is from: Applied Numerical Analysis (7th Edition) (Paperback)
Using the text for self study, I was initially quite pleased. The layout is attractive, selection of topics appropriate and writing style generally clear. The applied problems are rather nice.
While the derivation of the methods and theory discussed is generally brief- the author does provide an adequate basis for a workable understanding. Exposition is appropriate (perhaps even good) for an 'applied' book.
I did, however, find the work somewhat uneven: the Newton Cotes section, for example, was a little more disorganized than I would have liked. Some simple rearrangement and grouping of thoughts would have already helped to clarify many of the ideas. Surprisingly, the previous (6th) edition seems to have done a better job in this particular case.
In any event, my largest issue with the book is the staggering number of errors. I don't use the term lightly. I've read many technical books that have a minor typo here or there: it's natural. With Applied Numerical Analysis there appears to have been little proof-reading at all!
In Chapter 3 alone I've noted more than 10 problems: some more than simple typo's. This is unacceptable for a technical work!
I spent a great deal of time and effort trying to understand many of the discussions only to eventually realize that the cause of my frustration was a fault in the text. Besides the wasted effort, this had the knock-on effect that I began to doubt everything that seemed the least bit confusing.
Publishers should be reprimanded for such lax quality control.
If you do intend to use this book, I would recommend that you try to find a comprehensive list of errata somewhere.
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2 of 2 people found the following review helpful:
4.0 out of 5 stars
One of the very best numerical analysis books, September 26, 2009
This review is from: Applied Numerical Analysis (7th Edition) (Paperback)
I've owned a copy of this since I was an undergrad back in the late 1970's when it was just in its second edition. I haven't seen a book dedicated to the teaching of numerical analysis that explains algorithms more clearly. The authors go into great detail not just on the how's but the why's - the motivation of doing things a certain way. Strangely enough, though, the numerous mistakes just get worse with age, not better. My old original second edition printed in 1980 has relatively few errors. This seventh edition has errors to the point of distraction. If you must have this for a text you might want to also pick up a copy of the very economical
Introduction to Numerical Analysis: Second Edition (Dover Books on Advanced Mathematics) by Hillebrand. It's an oldie but a goodie. If you think Gerald's text is in error look up the topic in Hillebrand and insure you understand the topic. Chances are you do and there is a numerical error in Gerald's text that contradicts your own correct understanding. Finally, any student of numerical analysis simply must have a copy of
Numerical Recipes 3rd Edition: The Art of Scientific Computing. That one is more of the "give a man a fish" variety and has the source code and some explanation, but is by no means a textbook.
Oddly enough the table of contents is not included in the product description for this book, so I show that next just so you'll know what you're getting
0. Preliminaries.
Analysis versus Numerical Analysis.
Computers and Numerical Analysis.
An Illustrative Example.
Kinds of Errors in Numerical Procedures.
Interval Arithmetic.
Parallel and Distributed Computing.
Measuring the Efficiency of Procedures.
1. Solving Nonlinear Equations.
Interval Halving (Bisection).
Linear Interpolation Methods.
Newton's Method.
Muller's Method.
Fixed-Point Iteration.
Other Methods.
Nonlinear Systems.
2. Solving Sets of Equations.
Matrices and Vectors.
Elimination Methods.
The Inverse of a Matrix and Matrix Pathology.
Almost Singular Matrices - Condition Numbers.
Interactive Methods.
Parallel Processing.
3. Interpolation and Curve Fitting.
Interpolating Polynomials.
Divided Differences.
Spline Curves.
Bezier Curves and B-Splines.
Interpolating on a Surface.
Least Squares Approximations.
4. Approximation of Functions.
Chebyshev Polynomials and Chebyshev Series.
Rational Function Approximations.
Fourier Series.
5. Numerical Differentiation and Integration.
Differentiation with a Computer.
Numerical Integration - The Trapezoidal Rule.
Simpson's Rules.
An Application of Numerical Integration - Fourier Series and Fourier Transforms Adaptive Integration.
Gaussian Quadrature.
Multiple Integrals.
Applications of Cubic Splines.
6. Numerical Solution of Ordinary Differential Equations.
The Taylor Series Method.
The Euler Method and Its Modification.
Runge-Kutta Methods.
Multistep Methods.
Higher-Order Equations and Systems.
Stiff Equations.
Boundary-Value Problems.
Characteristic-Value Problems.
7. Optimization.
Finding the Minimum of y = f(x).
Minimizing a Function of Several Variables.
Linear Programming.
Nonlinear Programming.
Other Optimizations.
8. Partial Differential Equations.
Elliptic Equations.
Parabolic Equations.
Hyperbolic Equations.
9. Finite Element Analysis.
Mathematical Background.
Finite Elements for Ordinary Differential Equation.
Finite Elements for Partial Differential Equation.
Appendices.
A. Some Basic Information from Calculus.
B. Software Resources.
Answers to Selected Exercises.
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