I have a bit of an odd background. I have a fair bit of mathematics (four year MA equivalent course in mathematics at Cambridge) and at least a reasonable background in software engineering and programming (about three years working as a software engineer now, plus a lot of random stuff on my spare time during that period and a little bit before hand), but I don’t have a lot of knowldge of the overlap between the two. This is increasingly causing me trouble, and I’d like to fix it. It seems like the sort of subject my blog audience should know about, so I’m asking for help here. :-)

The immediate subject I want to learn more about is numerical linear algebra. It’s come up a couple times recently and I’ve had to go “Bwrgh. Um. Halp!”. I usually muddle through, but it’s really not something I should be struggling on and I’ve probably done stupid things as a result of lack of knowledge.

So, my goal here is to become reasonably well versed in at least the basics of the subject. At the moment nothing terribly specific – I want to get a good grasp of the theory and practice of working with matrices, vectors, etc. computationally. Linear optimisation and eigenvector problems especially. I’m looking for recommendations for books, libraries, software packages and anything else you think would be useful. I’m willing to spend a reasonable amount of money (more so on the books than the software packages, as long term I’ll really be looking for stuff I can freely bundle with my personal projects) in doing so, ‘though obviously free is a plus. Libraries I can use from a variety of languages are definitely a good thing, though I’m willing to look at language specific things like NumPy, etc. too if they come highly recommended (at least as a starting point).

Relevant background:

Mathematics: Quite a lot of real and complex analysis, though mostly pure. Enough linear algebra that I at least know where to start with it, though I’m going to be rusty.

Programming/computer science: Some amount of general algorithms and datastructures work. Generally comfortable with Java, Haskell and Scala. Comfortable enough with C that I can write it if I have to. A little bit of Python and Lua (plus a few others which are probably not relevant). Fairly willing to pick up a new language if it would help (though if you tell me to write fortran I’ll cry).

So, suggestions?

Edit: I’ll keep a list of recommendations updated here. If you have any comments for or against these, please pipe up.

I found a copy of Epperson going very cheaply and for no particular reason it looked interesting, so I’ve ordered a copy. I’ll almost certainly order a copy of Golub and Loan. I’m also going to be playing around with Octave. Thanks guys!