Customer Reviews

Introduction to Numerical Analysis

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The author offers this as an introductory book on the subject. Maybe so. But you had better have a solid background in classical analysis. On the level of Marsden's "Elementary Classical Analysis", for example.

Neumaier describes the various numerical methods from a more rigorous standpoint than most other books on numerical analysis. So, for example, you should already be acquainted with such ideas as a closed convex hull or the infinity norm. It is not totally theoretical. He shows the use of Maple for generating results. Though perhaps examples in Mathematica would also be useful.

The book is good for those of you who want a detailed treatment of the conceptual foundations of the field.

I teach a course in numerical methods approximately every two years and am always looking for "the ideal textbook." At this time I am using "Elementary Numerical Analysis: Third Edition" by Atkinson and Han. I examined this book to determine if it would be a better selection for the course.
This book covers all of the standard fare for the course:

*) Fundamental analysis of computer error
*) Solving linear systems of equations
*) Interpolation and numerical differentiation
*) Numerical integration
*) Solving nonlinear equations
*) Solving systems of nonlinear equations

The quality of the explanations is slightly weaker than in the Atkinson book, there is nothing specific to point to; I just find the Atkinson book more readable. Algorithms in both books are expressed in Matlab code, so there is no real difference there.
In conclusion, while I found that this book is certainly usable and may even be ranked as my second choice, at this time I will not be adopting in for use in my course.