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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 tex2html_wrap_inline149 , 0.6 seconds; for tex2html_wrap_inline119 , 1.3 seconds; for tex2html_wrap_inline123 , 4.5 seconds.

Time for Newton-isolating all the roots of modulus greater than 1: for tex2html_wrap_inline149 , 0.28 seconds; for tex2html_wrap_inline119 , 0.28 seconds; for tex2html_wrap_inline123 , 0.45 seconds.

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