Numerical analysis for complex arithmetic

[loinburger]

I'm trying to find a good book on numerical anlaysis for complex arithmetic, but all of the numerical analysis texts at the library only deal with real numbers, and all of the texts on complex arithmetic are either written for mathematicians (and hence they cover all of the theory I'm not interested in and none of the theory I'm interested in) or physicists ("use MATLAB"). There's probably a book hiding behind an inappropriate LC subject heading, but I'm not likely to find it without scouring the entire Q-section (which is many many stacks of books). Anybody have any texts they can suggest?

[Japher]

I'm surprised that there haven't been any replies!

[loinburger]

I didn't get any replies at the "Erotic Furry Roleplaying Forum" either.

[Japher]

maybe it's you

[BeBMan]

Isn't there some genius at work you could ask?

[Winston]

If it's for stopping a door, why not use a couple of wine corks?

[Ramo]

Never heard of a book like that, but you could try a generic complex analysis book in combination with "Numerical Recipes."

[loinburger]

Originally posted by BeBro
Isn't there some genius at work you could ask?

Somebody somewhere in the lab might be able to answer my question, but they sure as hell don't work in my branch. (I was going to give a hilarious example of what one of the people in my branch is working on, but unfortunately when you google for the topic + "air force" his name is in the first hit. )

Originally posted by Ramo
Never heard of a book like that, but you could try a generic complex analysis book in combination with "Numerical Recipes."

I'm primarily interested in how to improve the efficiency of switching back and forth between polar and cartesian coordinates, and Numerical Recipes only (briefly) covers cartesians. I'm operating on the assumption that somebody has developed a fancy way to reduce the truncation errors that you'd get by systematically calling the relevant trig functions, but I'm worried that the research may be proprietary (since it's the type of research for which a company making a math software library would shell out big bucks, and that wouldn't be sexy enough for a university researcher to bother with).

[Lul Thyme]

I think a lot of real numerical analysis is still applicable.
A lot of it deals with vector calculus and for many computations, complex arithmetic is real vector arithmetic with an extra operation (the multiplication).
For example your specific problem could be studied for the angle of optimizing trig variables on real variables no?