McMullen’s root-finding algorithm for cubic polynomials
Copyright policy )McMullen’s root-finding algorithm for cubic polynomials
Summary: We show that a generally convergent root-finding algorithm for cubic polynomials defined by \textit{C. McMullen} [Ann. Math. (2) 125, 467--493 (1987; Zbl 0634.30028)] 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.
- University of North Carolina at Chapel Hill United States
root-finding algorithms, Numerical computation of solutions to single equations, Functional equations in the complex plane, iteration and composition of analytic functions of one complex variable, Small divisors, rotation domains and linearization in holomorphic dynamics, complex dynamics, Dynamics of complex polynomials, rational maps, entire and meromorphic functions; Fatou and Julia sets
root-finding algorithms, Numerical computation of solutions to single equations, Functional equations in the complex plane, iteration and composition of analytic functions of one complex variable, Small divisors, rotation domains and linearization in holomorphic dynamics, complex dynamics, Dynamics of complex polynomials, rational maps, entire and meromorphic functions; Fatou and Julia sets
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