Be warned, there is no method of finding roots for polynomials with orders up to a few hundred that won't have some trouble with numerical stability.

You could try Math::Polynomial::Solve. Unfortunately it will usually require you to use Math::Complex, which means that you can't do arbitrary precision arithmetic. This may be a problem if accuracy is an issue. I'm going to guess that it is.

Googling around another promising approach is outlined in http://math-blog.com/2008/03/06/polynomial-root-finding-with-the-jenkins-traub-algorithm/. That link links to a JavaScript implementation at http://www.akiti.ca/PolyRootRe.html. What is nice about that solution is that it only uses real arithmetic, so you're able to use Math::BigFloat to address precision issues.

In your situation I would be inclined to try to translate the JavaScript solution into a Perl one. (I'd prefer that over the FORTRAN because a lot of the work in structuring the program has been done for you. Plus I find JavaScript easier to read.) I'd personally start with a semi-automated translation, and fix up issues by hand until I began getting the same results. If you don't know much about parsing, this won't work for you. Instead you could translate one routine at a time, and throw data at each to verify your translation before going on. (Expect to have a few sessions where you're getting drastically different results and have no idea why...)

Once you have a Perl translation then you can play around with Math::BigFloat to find the right precision to work at. I personally would aim for finding a precision which satisfied both that the solution multiplied out gives the original polynomial to some tolerance, and that doubling the precision doesn't change the calculated roots by more than a specified tolerance.

Be warned that this is likely to be a fair amount of work. But it will be less than trying to come up with something on your own, and it will be more likely to give correct answers.

In reply to Re: Internal Rate of Return by tilly
in thread Internal Rate of Return by ig

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