Measures of the Basins of Attracting n-Cycles for the Relaxed Newton’s Method

Gutiérrez, José Manuel; Hernández, Lidia; Magreñán, Á. Alberto; Rivas, M. T.

doi:10.1007/978-3-319-39228-8_9

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2018

2023

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Cited by 4 publications

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“…Very recently, in [13,14,15,16] the dynamical behavior of iterative methods for solving nonlinear equations with multiple roots is analyzed. The use of complex dynamics tools on these kind of problems is very fruitful, as their stability properties show.…”

Section: Introductionmentioning

confidence: 99%

Dynamical analysis on cubic polynomials of Damped Traub’s method for approximating multiple roots

Vázquez‐Lozano

Cordero

Torregrosa

2018

Applied Mathematics and Computation

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In this paper, the performance of a parametric family including Newton's and Traub's schemes on multiple roots is analyzed. The local order of convergence on nonlinear equations with multiple roots is studied as well as the dynamical behavior in terms of the damping parameter on cubic polynomials with multiple roots. The fixed and critical points, and the associated parameter plane are some of the characteristic dynamical features of the family which are obtained in this work. From the analysis of these elements we identify members of the family of methods with good numerical properties in terms of stability and efficiency both for finding the simple and multiple roots, and also other ones with very unstable behavior.

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Section: Introductionmentioning

confidence: 99%