Mastering Algorithms with Perl

Chapter 16. Numerical Analysis

I have tried to avoid long numerical computations, thereby following Riemann’s postulate that proofs should be given through ideas and not voluminous computations.

—David Hilbert ReportonNumberTheory(1897)

Traditional computer science algorithms have a nice, clean, methodical sequence of steps that describe how computers-in-the-abstract (any language, any platform) can accomplish a task. In this book, we’ve dirtied the study of algorithms a bit—we’ve shown you language-specific solutions in an attempt to achieve better and more practical solutions. In the preface, we said that when it comes to implementations, the devil is in the details—and nowhere is this more true than in numerical analysis.

In this chapter, we’ll tackle a few topics from numerical analysis. This is scientific computing, where we worry about the sixth decimal place and encounter problems common to many branches of science. These problems are widely applicable to other domains but are often overlooked because of their mathematical sophistication. We’ll do our best to make them palatable.

Let’s say you’re a webmaster for a large company. You’ve been dutifully keeping access logs, so you know how many people visit your site, and you know which pages they visit. Every week you rotate your log files. If you want to depict how the usage varies over time, it’s a simple matter to extract the data with Perl and plot a graph using the GD module. But what does that graph really mean? Can ...