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Rounding Errors in Algebraic Processes

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The first rule of numeric computation is that the answer is wrong, and the goal is to find out by how much. Even a number like 0.1 has no exact representation a computer's binary arithmetic - the number comes with an error already built in. When you start combining numbers (i.e. doing arithmetic), things just get worse.

This book addresses the two biggest areas of numeric computing: polynomials and linear matrix algebra. The first half of the book goes over a number of techniques for finding roots of polynomials, in the ways that give the most answers of the highest quality. The second half of the book discusses ill-conditioned linear systems and solution techniques that avoid common pitfalls.

Unfortunately, the book discusses these critical topics in terms of 1963 technology. A modern eye finds it jarring to see computer arithmetic described in base 10, when binary is the natural language of machines. Wilkinson discusses fixed-point arithmetic, which is still used heavily in computing for multimedia and embedded systems. His approach is haphazard, though; a more systematic development would have served fixed-point users much better.

In its day, I'm sure this book was current and practical. It's easy to see how the author has distilled more complex discussions into applicable analysis. A lot has happened between that day and this, however. Techniques have developed (and are still being developed), and expository techniques have improved for the topics that the book does cover. IEEE floating point has since become the standard, and demands discussion of its own.

The modern reader looking for a practical guide should keep looking.

Wilkinson's material shows up as classic problems in current numerical analysis texts. Can't beat the price.