Solution

Algorithm based on simultaneous iterations (Aberth's method) with cluster analysis (see [1]).

Program in Fortran 90 based on the multiprecision package MPFUN, by D. Bailey.

Machine used: IBM Risc 6000.

Time for Newton-isolating all the roots: for n=20, a=1, 2.3 seconds; for n=200, a=1, 15 seconds; for n=500, a=1, 18 seconds.

Dario Andrea Bini, Dipartimento di Matematica, via Buonarroti 2, 56127 Pisa, ITALY bini@dm.unipi.it October 15, 1996