roots and high-order polynomial

Hello
Has anyone looked at the behaviour of the (polynomial) roots function
for high-order polynomials ? I have an application which internally
searches for the roots of a polynomial. It works nicely for order less
than 20, and then has an erratic behaviour for upper values...

I looked into the source and I wondered that roots is based on the
eigenvalues of the companion matrix. For high-order, this latter is
rather sparse. Would it improve anything to compute the eigenvalues
using sparse solvers?

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Fabrice Silva
Laboratory of Mechanics and Acoustics - CNRS
31 chemin Joseph Aiguier, 13402 Marseille, France.