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.

For n=20, m=k=3, a=100i, time needed for Newton-isolating all the roots up to within a relative error for nonisolated roots: 3.8 seconds; with automatic detection of multiplicity: 7 seconds; time for isolating the roots of modulus greater than 1: 0.88 seconds.

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