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Solution

Algorithm based on simultaneous iterations (Aberth's method) with cluster analysis (D. Bini, Numerical computation of polynomial zeros by means of Aberth's method, to appear in Numerical Algorithms).

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

Machine used: IBM Risc 6000.

Time for isolating all the roots: for tex2html_wrap_inline101 , 0.88 seconds; for tex2html_wrap_inline93 , 1.22 seconds; for tex2html_wrap_inline97 , 4.6 seconds.

Time for Newton-isolating all the roots of modulus greater than 1: for tex2html_wrap_inline101 , 0.3 seconds; for tex2html_wrap_inline93 , 0.3 seconds; for tex2html_wrap_inline97 , 0.45 seconds.

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