Numerical method

I wrote a program to do arbitrary precision, non-integer power and root. Yes, I knew this wheel had already been invented, but I wanted to do it myself.

The program is very slow. The numerical method I'm using is exactly the same as what a person would do, in base 10, with pencil and paper. It has no limit on significant digits (except for the length of a string I can store in a variable, which is far more than I have the computer power to test anyway), but it is very slow.

What I want is a numerical method(s) to do it faster. I don't want programming code, I want to program it myself. What I want is the math method(s).

The numerical method(s) must be public domain, without any GNU, GPL, or similar restrictions.

If there is a method or methods that is even faster but limited in it's potential for how many significant digits of precision it could support (though able to go well beyond the usual 15 or so significant digits), I want to know that method too.

I don't have advanced math knowledge -- I didn't go any further than high-school pre-calculus, and that was a long time ago. I just enjoy programming math. I bought a used copy of the Numerical Methods book, but it made my eyes bleed. I'd probably have to study a lot more math to really understand that book.

I am not just looking for a list of names of numerical methods to use. I need you to show me the numerical method itself, not just tell me it's name.

If this request is unclear in any way, please ask for any clarification you need.

## Deliverables

1) A public domain numeric method or methods, with no GNU or similar restrictions, to do arbitrary precision non-integer power and root, where the power and root are high or arbitrary precision non-integers.

2) The numerical method(s) itself, not just a name of a numerical method.

2) All deliverables will be considered "work made for hire" under U.S. Copyright law. Buyer will receive exclusive and complete copyrights to all work purchased. (No GPL, GNU, 3rd party components, etc.).

## Platform

Windows XP and Vista

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