Superattracting cycles for some Newton type iterative methods

DOI10.1007/s11425-010-4141-1zbMath1218.37123OpenAlexW1992090409MaRDI QIDQ547380

Sergio Plaza, Emilie Navarro, Sergio Amat, Sonia Busquier

Publication date: 1 July 2011

Published in: Science China. Mathematics (Search for Journal in Brave)

Full work available at URL: http://hdl.handle.net/10533/128382

zbMATH Keywords

dynamicsiterative methods(super)attracting cycles

Mathematics Subject Classification ID

Iterative numerical methods for linear systems (65F10) Zeros of polynomials, rational functions, and other analytic functions of one complex variable (e.g., zeros of functions with bounded Dirichlet integral) (30C15) Dynamical systems in numerical analysis (37N30)

Related Items (3)

Superattracting cycles of the relaxed Newton's method for entire functions ⋮ Prescribed cycles of König's method for polynomials ⋮ Finite pairs of prescribed cycles of König's and Steffensen's methods for entire functions

Cites Work

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• On the iteration of a rational function: Computer experiments with Newton's method
• Extraneous fixed points, basin boundaries and chaotic dynamics for Schröder and König rational iteration functions
• Complex analytic dynamics on the Riemann sphere
• On the dynamics of some Newton's type iterative functions
• Julia Sets and Mandelbrot-Like Sets Associated With Higher Order Schroder Rational Iteration Functions: A Computer Assisted Study
• Attracting Orbits in Newton's Method
• Iteration of meromorphic functions
• A note on a family of newton type iterative processes
• A family of newton type iterative processes

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