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 up to within the relative error : 6.9 seconds; Time for isolating all the roots with automatic detection of multiplicities: 20 seconds.

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