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Numerical Methods and Optimization

Éric Walter
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The Basic Library List Committee suggests that undergraduate mathematics libraries consider this book for acquisition.

[Reviewed by
Allen Stenger
, on

This is a very erudite survey of numerical methods. The “Optimization” in the title is misleading: the book does cover optimization but does not have a special emphasis on it. The book teaches you how to analyze your problem and pick the best numerical method to solve it

It covers all the standard areas of numerical analysis. For each type of problem, it sketches the available techniques and gives their strengths and weaknesses and the best situations to use them. The book uses MATLAB; at the end of each chapter there are several worked examples, often contrasting different methods for the same problem. There are no theorems or proofs, and in most cases the book does not go into enough depth for you to learn how to use the method, but it gives references to works that do teach this. The chapter summaries are especially valuable, because they concentrate on advice rather than facts.

Two especially interesting parts of the book are the chapter on linear algebra, that gives a very clear guide to navigating your way through problems based on the structure of the matrix, and the chapter on errors in floating-point arithmetic, including some experimental ways to judge the size of the error in a large computation.

The book is primarily a reference, but it does include as the last chapter a set of 27 “problems given over the last 10 years to students as part of their final exam.”

Allen Stenger is a math hobbyist and retired software developer. He is an editor of the Missouri Journal of Mathematical Sciences. His mathematical interests are number theory and classical analysis.