Jenkins-Traub is widely used, but not state-of-the-art.
I assume that in translating it you found a number of ad-hoc tests.
(I have a version of JT that I translated from allroots into MPFR, which
would give you a major speedup
over the maxima code. see
http://www.cs.berkeley.edu/~fateman/generic/gmpjenkins.lisp and
..jenkins.lisp
But you would have to read in the MPFR library. I suppose it could use
the lisp bf library...
)
Anyway, people are working full time on clever, accurate, parallel, even
multiple-precision, eigenvalue computations, and with that, the
zero-finding becomes eigenvalues(polytocompanion(p,x));
I'll try to figure out who has done eigenvalue stuff we can use.
RJF
Raymond Toy (RT/EUS) wrote:
> Richard Fateman wrote:
>
>> I think the smart money on this computation is heading towards
>> finding the
>> eigenvalues of the companion matrix.
>
>
> Is it? I thought Jenkins-Traub was still pretty much state of the art.
>
> Ray