McMullen’s root-finding algorithm for cubic polynomials

Hawkins, Jane

doi:10.1090/S0002-9939-02-06659-5

McMullen’s root-finding algorithm for cubic polynomials
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by Jane M. Hawkins PDF

Proc. Amer. Math. Soc. 130 (2002), 2583-2592 Request permission

Abstract:

We show that a generally convergent root-finding algorithm for cubic polynomials defined by C. McMullen is of order 3, and we give generally convergent algorithms of order 5 and higher for cubic polynomials. We study the Julia sets for these algorithms and give a universal rational map and Julia set to explain the dynamics.

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