Cordero Barbero, Alicia; Leonardo Sepúlveda, Miguel A.; Torregrosa Sánchez, Juan Ramón(MDPI AG, 2022-10)
[EN] In this manuscript, we propose a parametric family of iterative methods of fourth-order convergence, and the stability of the class is studied through the use of tools of complex dynamics. We obtain the fixed and ...
[EN] In this manuscript, by using the weight-function technique, a new class of iterative methods for solving nonlinear problems is constructed, which includes many known schemes that can be obtained by choosing different ...
Chicharro López, Francisco Israel; Cordero Barbero, Alicia; Garrido-Saez, Neus; Torregrosa Sánchez, Juan Ramón(MDPI AG, 2019-05-06)
[EN] In this paper, a simple family of one-point iterative schemes for approximating the solutions of nonlinear equations, by using the procedure of weight functions, is derived. The convergence analysis is presented, ...
Cordero Barbero, Alicia; Maimó, Javier G.; Torregrosa Sánchez, Juan Ramón; Vassileva, María P.(MDPI AG, 2019-11)
[EN] Iterative methods for solving nonlinear equations are said to have memory when the calculation of the next iterate requires the use of more than one previous iteration. Methods with memory usually have a very stable ...
Artidiello Moreno, Santiago de Jesús; Chicharro López, Francisco Israel; Cordero Barbero, Alicia; Torregrosa Sánchez, Juan Ramón(Taylor & Francis Ltd, 2013-10)
In this paper, a family of new fourth-order optimal iterative methods for solving nonlinear equations is proposed. The classical King s family of fourth-order schemes is obtained as an special case. We also present results ...
[EN] In this study, an iterative scheme of sixth order of convergence for solving systems of nonlinear equations is presented. The scheme is composed of three steps, of which the first two steps are that of third order ...
Cordero Barbero, Alicia; García-Maimo, Javier; Torregrosa Sánchez, Juan Ramón; Vassileva, Maria P.(Springer-Verlag, 2017)
[EN] In this paper, we present a multidimensional real dynamical study of the Ostrowsky-Chun family of iterative methods to solve systems of nonlinear equations. This family was defined initially for solving scalar equations ...
[EN] There are few optimal fourth-order methods for solving nonlinear equations when the multiplicity in of the required loot is known in advance. Therefore, the first focus of this paper is on developing new fourth order ...
Babajee, Diyashvir K. R.; Cordero Barbero, Alicia; Soleymani, Fazlollah; Torregrosa Sánchez, Juan Ramón(Springer Verlag, 2014-01)
This paper presents an improvement of the sixth-order method of Chun and Neta as a class of three-step iterations with optimal efficiency index, in the sense of Kung-Traub conjecture. Each member of the presented class ...
Chicharro, Francisco I.; Cordero Barbero, Alicia; Garrido, Neus; Torregrosa Sánchez, Juan Ramón(Elsevier, 2022-05-15)
[EN] In this work, we start from a family of iterative methods for solving nonlinear multidimensional problems, designed using the inclusion of a weight function on its iterative
expression. A deep dynamical study of the ...
[EN] In this paper, we propose a family of iterative methods for finding multiple roots, with known multiplicity, by means of the introduction of four univariate weight functions. With the help of these weight functions, ...
Padilla, José J.; Chicharro, Francisco I.; Cordero Barbero, Alicia; Torregrosa Sánchez, Juan Ramón(MDPI AG, 2022-10)
[EN] Research interest in iterative multipoint schemes to solve nonlinear problems has increased recently because of the drawbacks of point-to-point methods, which need high-order derivatives to increase the order of ...
In this work, we extract some new and efficient two-point methods with memory from their corresponding optimal methods without memory, to estimate simple roots of a given nonlinear equation. Applying two accelerator ...
Amiri, A. R.; Cordero Barbero, Alicia; Darvishi, M. T.; Torregrosa Sánchez, Juan Ramón(Springer-Verlag, 2019-05)
[EN] The dynamical properties of a family of forward, central divided differences and Richardson extrapolation technique are studied. Applying these tools, an iterative method for solving nonlinear systems can be transformed ...
[EN] It is well known that scalar iterative methods with derivatives are highly more stable than their derivative-free partners, understanding the term stability as a measure of the wideness of the set of converging initial ...
Chicharro, Francisco I.; Cordero Barbero, Alicia; Garrido, Neus; Torregrosa Sánchez, Juan Ramón(Springer-Verlag, 2019-05)
[EN] Based on the third-order Traub's method, two iterative schemes with memory are introduced. The proper inclusion of accelerating parameters allows the introduction of memory. Therefore, the order of convergence of the ...
[EN] In the literature exist many iterative methods with memory for solving nonlinear equations, the most of them designed in the last years. As they use the information of (at least) the two previous iterates to generate ...
[EN] In this paper, we study the stability of the rational function associated to a known family of eighth-order iterative schemes on quadratic polynomials. The asymptotic behavior of the fixed points corresponding to the ...
[EN] There are several problems of pure and applied science which can be studied in the unified
framework of the scalar and vectorial nonlinear equations. In this paper, we propose a
sixth-order family of Jarratt type ...