Ebook: Lectures on finite precision computations

Interesting premise: instead of formulating mathematical problems in Real (or complex) space, formulate them instead in the space containing only those numbers representable on a computer. Surely, this is a very important point and one that deserves the *rigorous* mathematical treatment given in this book. Using computers forces us to have finite numbers, which introduces several little quirks when performing calculations on a computer- Chaitin-Chatelin and Fraysse make a stab at trying to quantify and understand said quirks by developing a mathematical framework in which to discuss the various issues that pop up. Taking what they gleaned from the theory, the latter half of the book is full of numerical experiments with a MATLAB tool written by the authors, investigating singularities, polynomial roots, and eigenvalues.

Fair warning: this text is very heavy on the math. I had to break out my numerical analysis book a few times. Throughout most of the book, I found myself thinking, "why bother?" as I often do when reading outer-space math works. Down here with the rest of us non-mathematicians, users of most practical computers codes don't care about the 15th significant figure of results. Nevertheless, it was still a fascinating read for me- and the subject matter should, of course, always be kept in mind when writing/working with number crunching codes.