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 isolating all the roots: 2.9 seconds;

Time for isolating only the real roots: 1.5 seconds;

Time for isolating the roots of modulus greater than 1: 1.5 seconds;

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