A first overview on the real dynamics of Chebyshev's method

DOI10.1016/j.cam.2016.02.040zbMath1357.65054OpenAlexW2292317412MaRDI QIDQ507912

José Manuel Gutiérrez Jimenez, Ángel Alberto Magreñán, Martín García-Olivo

Publication date: 9 February 2017

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cam.2016.02.040

zbMATH Keywords

Newton's methodHalley's methoditerative methodsnonlinear equationspolynomialroot-findingChebyshev's methodreal dynamicsFeigenbaum bifurcation diagrams

Mathematics Subject Classification ID

Numerical computation of roots of polynomial equations (65H04)

Cites Work

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• A new tool to study real dynamics: the convergence plane
• Graphic and numerical comparison between iterative methods
• A complex dynamical approach of Chebyshev's method
• Extraneous fixed points, basin boundaries and chaotic dynamics for Schröder and König rational iteration functions
• Real qualitative behavior of a fourth-order family of iterative methods by using the convergence plane
• Dynamics of a family of Chebyshev-Halley type methods
• On Schröder's families of root-finding methods
• NEWTON'S VERSUS HALLEY'S METHOD: A DYNAMICAL SYSTEMS APPROACH
• Julia sets for the super-Newton method, Cauchy’s method, and Halley’s method

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