Dynamics and fractal dimension of Steffensen-type methods

DOI10.3390/A8020271zbMath1461.65075OpenAlexW1521743511MaRDI QIDQ1736654

Alicia Cordero, Francisco I. Chicharro, Juan Ramón Torregrosa Sánchez

Publication date: 26 March 2019

Published in: Algorithms (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3390/a8020271

zbMATH Keywords

nonlinear equationfractal dimensiondynamical planederivative-freePadé-like approximant

Mathematics Subject Classification ID

Conformal densities and Hausdorff dimension for holomorphic dynamical systems (37F35) Numerical computation of solutions to single equations (65H05) Hausdorff and packing measures (28A78)

Related Items (4)

Derivative free iterative methods with memory having higher R-order of convergence ⋮ King-type derivative-free iterative families: real and memory dynamics ⋮ A study on the local convergence and dynamics of the two-step and derivative-free Kung-Traub's method ⋮ Finite pairs of prescribed cycles of König's and Steffensen's methods for entire functions

Cites Work

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• An analysis of a new family of eighth-order optimal methods
• The ``Gauss-Seidelization of iterative methods for solving nonlinear equations in the complex plane
• Basins of attraction for several methods to find simple roots of nonlinear equations
• A class of Steffensen type methods with optimal order of convergence
• Graphic and numerical comparison between iterative methods
• On two families of high order Newton type methods
• Complex dynamics of derivative-free methods for nonlinear equations
• A new technique to obtain derivative-free optimal iterative methods for solving nonlinear equations
• Complex analytic dynamics on the Riemann sphere
• Fractal Basins of Attraction Associated with a Damped Newton's Method
• Optimal Order of One-Point and Multipoint Iteration

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