Chicharro, Francisco I.; Cordero Barbero, Alicia; Garrido-Saez, Neus; Torregrosa Sánchez, Juan Ramón(Taylor & Francis, 2019-10-03)
[EN] A bi-parametric family of iterative schemes for solving nonlinear systems is presented. We prove for any value of parameters the sixth-order of convergence of any members of the class. The efficiency and computational ...
Chicharro, Francisco I.; Cordero Barbero, Alicia; Garrido, Neus; Torregrosa Sánchez, Juan Ramón(John Wiley & Sons, 2020-01-12)
[EN] The stability analysis of a new family of iterative methods with memory is introduced. This family, designed from Traub's method, allows to add memory through the introduction of an accelerating parameter. Hence, the ...
[EN] In this paper, using the idea of weight functions on the Potra¿Pták method, an optimal fourth order method, a non optimal sixth order method, and a family of optimal eighth order methods are proposed. These methods ...
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)
Chicharro, Francisco I.; Garrido, Neus; Sarría, Íñigo; Orcos, Lara(Servicio de Publicaciones de la Universidad de Oviedo, 2021-06-18)
[EN] A technique for generating iterative methods for solving nonlinear equations with memory can be constructed
from a method without memory that includes a parameter, provided the parameter is present in the error ...
Garrido Saez, Neus(Universitat Politècnica de València, 2020-09-02)
[ES] El diseño de métodos iterativos para resolver ecuaciones y sistemas de ecuaciones no lineales es una tarea importante y desafiante en el campo del Análisis Numérico. La no linealidad es una característica de muchos ...
Chicharro, Francisco I.; Cordero Barbero, Alicia; Garrido-Saez, Neus; Torregrosa Sánchez, Juan Ramón(MDPI AG, 2019-12)
[EN] A generalized high-order class for approximating the solution of nonlinear systems of equations is introduced. First, from a fourth-order iterative family for solving nonlinear equations, we propose an extension to ...
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, ...
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 ...
Chicharro, Francisco I.; Cordero Barbero, Alicia; Garrido, Neus; Torregrosa Sánchez, Juan Ramón(MDPI AG, 2020-02)
[EN] In this work, two Traub-type methods with memory are introduced using accelerating parameters. To obtain schemes with memory, after the inclusion of these parameters in Traub's method, they have been designed using ...
[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 ...
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 ...
Chicharro, Francisco I.; Cordero Barbero, Alicia; Garrido, Neus; Torregrosa Sánchez, Juan Ramón(Elsevier, 2020-06)
[EN] Iterative methods with memory for solving nonlinear systems have been designed. For approximating the accelerating parameters the Kurchatov's divided difference is used as an approximation of the derivative of second ...
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 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 ...