[EN] A general optimal iterative method, for approximating the solution of nonlinear equations, of (n+1) steps with 2(n+1) order of convergence is presented. Cases n=0 and n=1 correspond to Newton's and Ostrowski's schemes, ...
[EN] In this manuscript, we propose an iterative step that, combined with any other method, allows us to obtain an iterative scheme for approximating the simple roots of a polynomial simultaneously. We show that adding ...
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 ...
Triguero Navarro, Paula(Universitat Politècnica de València, 2023-06-16)
[ES] En gran cantidad de problemas de la matemática aplicada, existe la necesidad de resolver ecuaciones y sistemas no lineales, dado que numerosos problemas, finalmente, se reducen a estos. Conforme aumenta la dificultad ...
[EN] In this paper, we propose a procedure that can be added to any iterative scheme in order to turn it into an iterative method for approximating all roots simultaneously of any nonlinear equations. By applying this ...
[EN] In this paper, we study different ways for introducing memory to a parametric family of optimal two-step iterative methods. We study the convergence and the stability, by means of real dynamics, of the methods obtained ...
[EN] In this paper, new tools for the dynamical analysis of iterative schemes with memory for solving nonlinear systems of equations are proposed. These tools are in concordance with those of the scalar case and provide ...