Finding all complex zeros of a high-degree polynomial Given a large univariate polynomial, say of degree 200 or more, is there a procedural way of finding all the complex roots? By "roots", I mean complex decimal approximations to the roots, though the multiplicity of the root is important. I have access to MAPLE and the closest function I've seen is:
with(RootFinding):
Analytic(Z,x,-(2+2*I)..2+2*I);

but this chokes if Z is of high degree (in fact it fails to complete even if deg(Z)>15). 

I think one of the biggest problems is approximating multiple roots. The approach described in
L.Brugnano, D.Trigiante. "Polynomial Roots: the Ultimate Answer?", Linear Algebra and its Applications 225 (1995) 207-219
relies on the approximation of eigenvalues of a tridiagonal matrix, obtained via the application of Euclid's GCD algorithm to the original polynomial, and seems to work pretty well.
I couldn't find the pdf for the article though, sorry.
