McMullen’s root-finding algorithm for cubic polynomials

DOI10.1090/S0002-9939-02-06659-5zbMath1075.37012OpenAlexW1578354568MaRDI QIDQ4330583

Jane M. Hawkins

Publication date: 13 May 2002

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0002-9939-02-06659-5

zbMATH Keywords

complex dynamicsroot-finding algorithms

Mathematics Subject Classification ID

Functional equations in the complex plane, iteration and composition of analytic functions of one complex variable (30D05) Small divisors, rotation domains and linearization in holomorphic dynamics (37F50) Numerical computation of solutions to single equations (65H05) Dynamics of complex polynomials, rational maps, entire and meromorphic functions; Fatou and Julia sets (37F10)

Related Items (2)

A Padé family of iterations for the matrix sector function and the matrix p th root ⋮ A root-finding algorithm for cubics

Cites Work

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• On the existence of generally convergent algorithms
• Extraneous fixed points, basin boundaries and chaotic dynamics for Schröder and König rational iteration functions
• Families of rational maps and iterative root-finding algorithms
• Rational iteration: complex analytic dynamical systems
• On the efficiency of algorithms of analysis
• Julia sets for the super-Newton method, Cauchy’s method, and Halley’s method

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