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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

McMullen's root-finding algorithm for cubic polynomials


Author: Jane M. Hawkins
Journal: Proc. Amer. Math. Soc. 130 (2002), 2583-2592
MSC (2000): Primary 37F10, 37D20; Secondary 49M99
Published electronically: April 22, 2002
MathSciNet review: 1900865
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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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Additional Information

Jane M. Hawkins
Affiliation: Department of Mathematics, CB #3250, University of North Carolina at Chapel Hill, Chapel Hill, North Carolina 27599
Email: jmh@math.unc.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-02-06659-5
PII: S 0002-9939(02)06659-5
Keywords: Root-finding algorithms, complex dynamics
Received by editor(s): January 11, 2001
Published electronically: April 22, 2002
Communicated by: Michael Handel
Article copyright: © Copyright 2002 American Mathematical Society