numerical recipes

Numerical Recipes, particularly the code in it, has something of a mixed reputation. Numerical methods are very hard for a layman such as myself to assess: Are they fast? Are they stable?

Many specialists think they're not. One example is the page Why not use Numerical Recipes? on (sorry, I know you don't like URLs on E2) http://math.jpl.nasa.gov/nr/. I've also heard doubts expressed by a numerical analyst. Frankly, not being an expert on the subject, I'm not sure.

They do do a good job of explaining the bare facts of each type of problem. Certainly (in my experience) enough to give you the vocabulary you need to seek out more specific help. But you'll probably want to consult a numerical analyst regarding the specifics of your problem before using their codes; other codes are often also available, e.g. at Netlib.

"Numerical Recipes" is the name of a series of books oft cited and frequently cursed by computer programmers the world over.

The purpose of this set of books is to be a reference for statistical and numerical algorithms used commonly in data proccessing and scientific computing. It covers things like:

• root finding
• curve fitting
• monte carlo integration
• computing variance, correlation, and other statisical functions
• pseudo-random number generators
• sorting
• Fourier transforms

As well as a host of other common problems, and the occasional geek-oriented commentary on the world. I quote from the introduction to the chapter on statistical description of data (italics are theirs) chosen to show the entertaining and whimsical nature of some of the accompanying text:

"If a statistic falls in a reasonable part of the distribution, you must not make the mistake of concluding that the null hypothesis is 'verified' or 'proved.' That is the curse of statistics, that it can never prove things, only disprove them! At best, you can substantiate a hypothesis by ruling out, statistically, a whole long list of competing hypotheses, every one that has ever been proposed. After a while your adversaries and competitors will give up trying to think of alternative hypotheses, or else they will grow old and die, and then your hypothesis will become accepted. Sounds crazy, we know, but that's how science works!"

The books take the form of describing an algorithm and then showing a sample implementation. The descriptions are brief and a little dense, but very helpful because they are a good starting point to go look for more information. The example code, however (at least in the C version of the book) is next to useless for a variety of reasons (including the fact that because the code is essentially just translated from FORTRAN all the arrays are treated as 1 based). That being said, the practical and concise description of the methods still make the book more than worth it.

The one I have handy is "Numerical Recipes in C (2nd Edition)", it's written by William H. Press, Saul A. Teukolsky, William T. Vetterling, and Brian P. Flannery and publised by Cambridge University Press.