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A new fourth-order family for solving nonlinear problems and its dynamics
(Journal of Mathematical Chemistry, 2015-03)
In this manuscript, a new parametric class of iterative methods for solving nonlinear systems of equations is proposed. Its fourth-order of convergence is proved and a dynamical analysis on low-degree polynomials is made ...
Local Convergence and the Dynamics of a Two-Step Newton-Like Method
(International Journal of Bifurcation and Chaos in Applied Sciences and Engineering, 2016-05)
We present the local convergence analysis and the study of the dynamics of a two-step Newton-like method in order to approximate a locally unique solution of multiplicity one of a nonlinear equation.
On the local convergence and the dynamics of Chebyshev–Halley methods with six and eight order of convergence
(Journal of Computational and Applied Mathematics, 2016-05)
We study the local convergence of Chebyshev–Halley methods with six and eight order of convergence to approximate a locally unique solution of a nonlinear equation. In Sharma (2015) (see Theorem 1, p. 121) the convergence ...
A first overview on the real dynamics of Chebyshev's method
(Journal of Computational and Applied Mathematics, 2017-07)
In this paper we explore some properties of the well known root-finding Chebyshev’s method applied to polynomials defined on the real field. In particular we are interested in showing the existence of extraneous fixed ...
Local convergence of a relaxed two-step Newton like method with applications
(Journal of Mathematical Chemistry, 2017-08)
We present a local convergence analysis for a relaxed two-step Newton-like method. We use this method to approximate a solution of a nonlinear equation in a Banach space setting. Hypotheses on the first Fr,chet derivative ...
New improved convergence analysis for Newton-like methods with applications
(Journal of Mathematical Chemistry, 2017-08)
We present a new semilocal convergence analysis for Newton-like methods using restricted convergence domains in a Banach space setting. The main goal of this study is to expand the applicability of these methods in cases ...
Convergence of Newton's method under Vertgeim conditions: new extensions using restricted convergence domains
(Journal of Mathematical Chemistry, 2017-08)
We present new sufficient convergence conditions for the semilocal convergence of Newton’s method to a locally unique solution of a nonlinear equation in a Banach space. We use Hölder and center Hölder conditions, instead ...
Local convergence for multi-point-parametric Chebyshev–Halley-type methods of high
(Journal of Computational and Applied Mathematics, 2015-07)
We present a local convergence analysis for general multi-point-Chebyshev-Halley-type methods (MMCHTM) of high convergence order in order to approximate a solution of an equation in a Banach space setting. MMCHTM includes ...
A biparametric extension of King’s fourth-order methods and their dynamics
(Applied Mathematics and Computation, 2016-05)
A class of two-point quartic-order simple-zero finders and their dynamics are investigated in this paper by extending King’s fourth-order family of methods. With the introduction of an error corrector having a weight ...
Stability analysis of a parametric family of iterative methods for solving nonlinear models
(Applied Mathematics and Computation, 2016-07)
A one-parametric family of fourth-order iterative methods for solving nonlinear systems is presented, proving the fourth-order of convergence of all members in this family, except one of them whose order is five. The methods ...