A comparison between iterative methods by using the basins of attraction

DOI10.1016/J.AMC.2011.05.055zbMath1252.65086OpenAlexW2044149156MaRDI QIDQ658659

Gheorghe Ardelean

Publication date: 13 January 2012

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

Full work available at URL: https://doi.org/10.1016/j.amc.2011.05.055

zbMATH Keywords

convergencenumerical examplesnonlinear equationsbasins of attractioncomplex coefficients polynomialimproved iterative methods

Mathematics Subject Classification ID

Zeros of polynomials, rational functions, and other analytic functions of one complex variable (e.g., zeros of functions with bounded Dirichlet integral) (30C15) General theory of numerical methods in complex analysis (potential theory, etc.) (65E05) Numerical computation of roots of polynomial equations (65H04)

Related Items (10)

Applications of accelerated computational methods for quasi-nonexpansive operators to optimization problems ⋮ Unification of sixth-order iterative methods ⋮ On the complex dynamics of continued and discrete Cauchy's method ⋮ On improved three-step schemes with high efficiency index and their dynamics ⋮ Estimating the Hausdorff-Besicovitch dimension of boundary of basin of attraction in helicopter trim ⋮ Polynomiography for the polynomial infinity norm via Kalantari's formula and nonstandard iterations ⋮ Bisheh-Niasar-Saadatmandi root finding method via the \(S\)-iteration with periodic parameters and its polynomiography ⋮ Convergence and dynamics of structurally identical root finding methods ⋮ A new third-order Newton-type iterative method for solving nonlinear equations ⋮ Higher order methods of the basic family of iterations via \(S\)-iteration scheme with \(s\)-convexity

Cites Work

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• Graphic and numerical comparison between iterative methods
• Newton's method's basins of attraction revisited
• A new two-step biparametric family of sixth-order iterative methods free from second derivatives for solving nonlinear algebraic equations
• Eighth-order methods with high efficiency index for solving nonlinear equations
• A family of fifth-order iterations composed of Newton and third-order methods
• From third to fourth order variant of Newton's method for simple roots
• Some higher-order modifications of Newton's method for solving nonlinear equations
• Some new variants of Newton's method.
• Some fourth-order modifications of Newton's method
• Fractal Newton basins
• A variant of Newton's method with accelerated third-order convergence

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