Newton-isolate all the roots of modulus greater than 1.
Newton isolating the roots means to compute approximations to
the roots
,
such that
for any
. In this way Newton's iteration applied to
converges
quadratically right from the start to
, i.e., for the approximation
obtained after k Newton's
steps with
, it holds
(compare P. Tilli, Convergence conditions of some methods for the
simultaneous computation of polynomial zeros, Calcolo 1996).