On the Julia set of König’s root–finding algorithms

DOI10.1090/S0002-9939-2013-11636-9zbMath1283.37046OpenAlexW2087972187WikidataQ122395308 ScholiaQ122395308MaRDI QIDQ2845435

Gerardo Honorato

Publication date: 30 August 2013

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

Full work available at URL: https://doi.org/10.1090/s0002-9939-2013-11636-9

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) Dynamics of complex polynomials, rational maps, entire and meromorphic functions; Fatou and Julia sets (37F10) Numerical computation of roots of polynomial equations (65H04)

Related Items

Dynamics and limiting behavior of Julia sets of König's method for multiple roots, The Julia sets of Chebyshev's method with small degrees, Regions of convergence and dynamics of Schröder-like iteration formulae as applied to complex polynomial equations with multiple roots, Prescribed cycles of König's method for polynomials, Symmetries of the Julia sets of König's methods for polynomials, On the global convergence of Schröder's iteration formula for real zeros of entire functions, On the global convergence of Schröder's iterative formulae for real roots of algebraic equations, Estimating convergence regions of Schröder's iteration formula: how the Julia set shrinks to the Voronoi boundary, Disconnected Julia set of Halley's method for exponential maps

Cites Work

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• Normal families
• Immediate and virtual basins of Newton's method for entire functions.
• On K nig's root-finding algorithms*
• On the Geometry of Halley's Method
• How to find all roots of complex polynomials by Newton's method.