Finding only some roots of a polynomial

[Pablo]

Hi everyone!

I need to find the roots of some quite big polynomials (order ~800). The
root function works fine (and surprisingly fast!), but I don't think
it's the best tool forwhat I need. I'm only interested in those roots
with high absolute value, so after "roots" works hard to find the 800
complex values, I discard almost all of them.

Do you have any suggestion for an algorithm to do that?

I did find a book on the subject (McNamee - Numerical Methods for Roots
of Polynomials, Vol1 - 2007), and it suggest (I didn't read it
thoroughly, yet) that the companion method finds the roots one by one,
starting with the one with the largest magnitude. However, there are a
multitude of similar methods in the book.

Is Octave doing that?

In that case I might try to modify the function to stop after a few
roots. I peeked in the source code, but I don't know Fortran, so it's
kind of hard to understand what is going on.

For reference, my current script is
  %lenght(c) is ~800
  r=roots(c)'; %This takes quite long
  %I only keep roots with abs(r)>=0 and angle(r)>=0
  P=abs(r);
  I=find(P>=1);
  BB=log(P(I))/deltat;
  WW=angle(r(I))/deltat;
  I=find(WW>=0);
  B=BB(I);
  W=WW(I);
  %Now lenght(W) is just around 10

Thank you very much for your answers, and for maintaining this great
program!
  Arnoques