For the discussion of math. Duh.
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When using Aberth's method for approximation of polynomial roots, are there any restrictions on the values of the initial seeds? Various root-finding methods are known to fail when the initial seeds are ill-conditioned in some manner (such as Durand-Kerner's inability to find non-real roots when the coefficients and all initial seeds are real), but I can't find anything describing bad seeds for the Aberth method.
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I used Aberth a while back. I found the upper and lower bounds on the modulus of the roots via Rouche, took the geometric mean and placed the roots evenly around the circle of that radius and got good convergence. But remember, try to get rid of the repeated roots first, because you will get bad convergence there.
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