[EN] In this paper, we analyze the stability of the family of iterative methods designed by Jarratt using complex dynamics tools. This allows us to conclude whether the scheme known as Jarratt's method is the most stable ...
The parameter space associated to the parametric family of Chebyshev-Halley on quadratic polynomials shows a dynamical richness worthy of study. This analysis has been initiated by the authors in previous works. Every value ...
Cordero Barbero, Alicia; Franques, Antonio; Torregrosa Sánchez, Juan Ramón(Springer-Verlag, 2016)
[EN] In this paper, a family of parametric iterative methods for solving nonlinear equations, including Homeier's scheme, is presented. Its local convergence is obtained and the dynamical behavior on quadratic polynomials ...
[EN] In this paper, we present a new parametric family of three-step iterative for solving nonlinear equations. First, we design a fourth-order triparametric family that, by holding only one of its parameters, we get to ...
Cordero Barbero, Alicia; García Maimo, Javier; Torregrosa Sánchez, Juan Ramón; Vassileva, María Penkova; Vindel Cañas, Pura(Elsevier, 2013-08)
In this paper, the dynamics of King's family of iterative schemes for solving nonlinear equations is studied. The parameter spaces are presented, showing the complexity of the family. The analysis of the parameter space ...
Cordero Barbero, Alicia; Guasp, Lucia; Torregrosa Sánchez, Juan Ramón(Elsevier, 2018)
[EN] In this manuscript, we analyze the dynamical anomalies of a parametric family of iterative schemes designed by Kou et al. It is known that its order of convergence is three for any arbitrary value of the parameter, ...
Chicharro, Francisco I.; Cordero Barbero, Alicia; Martínez, Tobías H.; Torregrosa Sánchez, Juan Ramón(Springer-Verlag, 2020-03)
[EN] The third-order iterative method designed by Weerakoon and Fernando includes the arithmetic mean of two functional evaluations in its expression. Replacing this arithmetic mean with different means, other iterative ...
Cordero Barbero, Alicia; Guasp, Lucia; Torregrosa Sánchez, Juan Ramón(Springer-Verlag, 2018)
[EN] A family of fourth-order iterative methods without memory, for solving nonlinear systems, and its seventh-order extension, are analyzed. By using complex dynamics tools, their stability and reliability are studied by ...
Chicharro López, Francisco Israel; Cordero Barbero, Alicia; Gutiérrez, José M.; Torregrosa Sánchez, Juan Ramón(Elsevier, 2013-02-15)
The dynamical behavior of two iterative derivative-free schemes, Steffensen and M4 methods, is studied in case of quadratic and cubic polynomials. The parameter plane is analyzed for both procedures on quadratic polynomials. ...
[EN] In this paper, we propose a general class of fourth-order optimal multi-point methods without
memory for obtaining simple roots. This class requires only three functional evaluations (viz.
two evaluations of function ...
Cordero Barbero, Alicia; Maimo, Javier G.; Rodríguez-Cabral, Antmel; Torregrosa Sánchez, Juan Ramón(MDPI AG, 2023-03)
[EN] In this manuscript, we carry out a study on the generalization of a known family of multipoint scalar iterative processes for approximating the solutions of nonlinear systems. The convergence analysis of the proposed ...
Cordero Barbero, Alicia; Villalba, Eva G.; Torregrosa Sánchez, Juan Ramón; Triguero-Navarro, Paula(MDPI AG, 2021-01-03)
[EN] A new parametric class of iterative schemes for solving nonlinear systems is designed.
The third- or fourth-order convergence, depending on the values of the parameter being proven.
The analysis of the dynamical ...
Cordero Barbero, Alicia; Ferrero-Molina, Alfredo; Torregrosa Sánchez, Juan Ramón(Elsevier, 2016-01)
[EN] In this paper, a parametric family including Newton's and Traub's iterative schemes is presented. Its local convergence and dynamical behavior on quadratic polynomials are studied. The analysis of fixed and critical ...
Candelario, Giro; Cordero Barbero, Alicia; Torregrosa Sánchez, Juan Ramón; Vassileva, María P.(MDPI AG, 2023-08)
[EN] In this manuscript, we use approximations of conformable derivatives for designing iterative methods to solve nonlinear algebraic or trascendental equations. We adapt the approximation of conformable derivatives in ...
Chicharro López, Francisco Israel; Cordero Barbero, Alicia; Torregrosa Sánchez, Juan Ramón(Elsevier, 2013-04)
From position and velocity coordinates for several given instants, it is possible to determine the orbital elements of the preliminary orbit, taking only into account mutual gravitational attraction forces between the Earth ...
[EN] The construction of derivative-free iterative methods for approximating multiple roots of a nonlinear equation is a relatively new line of research. This paper presents a novel family of one-parameter second-order ...
Chicharro, Francisco I.; Cordero Barbero, Alicia; Garrido, N.; Torregrosa Sánchez, Juan Ramón(R. Company, J. C. Cortés, L. Jódar and E. López-Navarro, 2019-07-12)
Artidiello, S.; Cordero Barbero, Alicia; Torregrosa Sánchez, Juan Ramón; Vassileva, M. P.(Elsevier, 2017)
[EN] In this paper, a three-step iterative method with sixth-order local convergence for approximating the solution of a nonlinear system is presented. From Ostrowski¿s scheme adding one step of Newton with ¿frozen¿ ...
Artidiello Moreno, Santiago de Jesús; Cordero Barbero, Alicia; Torregrosa Sánchez, Juan Ramón; Vassileva, M.P.(Hindawi Publishing Corporation, 2015)
We present two classes of iterative methods whose orders of convergence are four and five, respectively, for solving systems of nonlinear equations, by using the technique of weight functions in each step. Moreover, we ...