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Dynamical and numerical analysis of classical multiple roots finding methods applied for different multiplicities
(Springer Nature, 2024-05-08)
The aim of this paper is the study of the robustness of classical methods defined for finding multiple roots with single multiplicity m when they are used for approximating different roots of a function having different ...
Archetypal Curves in the Shape and Size Space: Discovering the Salient Features of Curved Big Data by Representative Extremes
(Springer, 2023)
Curves are complex data. Tools for visualizing, exploring, and discovering the structure
of a data set of curves are valuable. In this paper, we propose a scalable methodology to
solve this challenge. On the one hand, ...
Convergence regions for the Chebyshev–Halley family
(Elsevier, 2018-03)
In this paper we study the dynamical behavior of the Chebyshev–Halley methods on the family of degree n polynomials . We prove that, despite increasing the degree, it is still possible to draw the parameter space by using ...
Connectivity of the Julia set for the Chebyshev-Halley family on degree n polynomials
(Elsevier, 2020-03)
We study the Chebyshev-Halley family of root finding algorithms from the point of view of holomorphic dynamics. Numerical experiments show that the speed of convergence to the roots may be slower when the basins of attraction ...
Dynamics of Newton-like root finding methods
(Springer, 2022)
When exploring the literature, it can be observed that the operator obtained when
applying Newton-like root finding algorithms to the quadratic polynomials z2 − c
has the same form regardless of which algorithm has been ...
Dynamics of a Family of Rational Operators of Arbitrary Degree
(Vilnius Gediminas Technical University, 2021-05-26)
. In this paper we analyse the dynamics of a family of rational operators
coming from a fourth-order family of root-finding algorithms. We first show that
it may be convenient to redefine the parameters to prevent ...
Dynamical analysis of an iterative method with memory on a family of third-degree polynomials
(AIMS Press, 2022)
Qualitative analysis of iterative methods with memory has been carried out a few years ago. Most of the papers published in this context analyze the behaviour of schemes on quadratic polynomials. In this paper, we accomplish ...
Dynamics of subfamilies of Ostrowski–Chun methods
(Elsevier, 2020-09-25)
In this paper, we classify the fixed and critical points of the bi-parametric family of Ostrowski–Chun methods applied onquadratic polynomials. We obtain the values of the parameters that reduce the number ...
Dynamical Analysis to Explain the NumericalAnomalies in the Family of Ermakov-KalitkinType Methods
(Vilnius Gediminas Technical University (VGTU) Press, 2019)
In this paper, we study the dynamics of an iterative method based onthe Ermakov-Kalitkin class of iterative schemes for solving nonlinear equations. Asit was proven in ”A new family of iterative methods widening areas of ...