Vázquez-Lozano, Juan Enrique; Cordero Barbero, Alicia; Torregrosa Sánchez, Juan Ramón(Elsevier, 2018)
[EN] In this paper, the performance of a parametric family including Newton¿s and Traub¿s schemes on multiple roots is analyzed. The local order of convergence on nonlinear equations with multiple roots is studied as well ...
Cordero Barbero, Alicia; Torregrosa Sánchez, Juan Ramón; Vindel, Pura(Vilnius Gediminas Technical University, 2019)
[EN] In this paper, we study the dynamics of an iterative method based on the Ermakov-Kalitkin class of iterative schemes for solving nonlinear equations. As it was proven in "A new family of iterative methods widening ...
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 ...
In this paper, the dynamics of the Chebyshev-Halley family is studied on quadratic polynomials. A singular set, that we call cat set, appears in the parameter space associated to the family. This set has interesting ...
In this paper, a complex dynamical study of a parametric Chebyshev-Halley type family of iterative methods on quadratic polynomial is presented. The stability of the fixed points is analyzed in terms of the parameter of ...
Campos, B.; Cordero Barbero, Alicia; Torregrosa Sánchez, Juan Ramón; Vindel, P.(Taylor & Francis (Routledge): STM, Behavioural Science and Public Health Titles, 2015-09-02)
In this paper, the dynamics of the family of c-iterative methods for solving nonlinear equations are studied on quadratic polynomials. A singular parameter space is presented to show the complexity of the family. The ...
Moscoso Martínez, Marlon Ernesto(Universitat Politècnica de València, 2020-09-02)
[ES] En el presente trabajo se estudia la dinámica compleja de una familia de métodos con esquemas iterativos multipaso, que es una generalización de un método propuesto por Artidiello y col., sobre polinomios cuadráticos. ...
Mora Jiménez, María(Universitat Politècnica de València, 2019-07-30)
[ES] Existen problemas no lineales con soluciones de multiplicidad superior a 1. Ello nos obliga a utilizar técnicas iterativas adaptadas a este tipo de problemas y a diseñar
nuevas técnica que mejoren las ya existentes, ...
Chicharro, Francisco I.; Cordero Barbero, Alicia; Garrido-Saez, Neus; Torregrosa Sánchez, Juan Ramón(John Wiley & Sons, 2023-05-11)
[EN] In this work, we modify the iterative structure of Traub's method to include a real parameter alpha$$ \alpha $$. A parametric family of iterative methods is obtained as a generalization of Traub, which is also a member ...
Behl, Ramandeep; Cordero Barbero, Alicia; Torregrosa Sánchez, Juan Ramón(Elsevier, 2022-05-15)
[EN] In this manuscript, we design an efficient sixth-order scheme for solving nonlinear
systems of equations, with only two steps in its iterative expression. Moreover, it belongs
to a new parametric class of methods whose ...
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] A set of multistep iterative methods with increasing order of convergence is presented, for solving systems of nonlinear equations. One of the main advantages of these schemes is to achieve high order of convergence ...
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 ...
[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 ...
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 ...
Singh, Sukhjit; Gupta, D. K.; Badoni, Rakesh P.; Martínez Molada, Eulalia; Hueso Pagoaga, José Luís(Springer-Verlag, 2017)
[EN] The local convergence analysis of a parameter based iteration with Hölder continuous first derivative is studied for finding solutions of nonlinear equations in Banach spaces. It generalizes the local convergence ...
[EN] Let Ax = b be a large and sparse system of linear equations where A is a nonsingular matrix. An approximate solution is frequently obtained by applying preconditioned terations. Consider the matrix B = A + PQT where ...
[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 ...
Cevallos Alarcón, Fabricio Alfredo(Universitat Politècnica de València, 2023-05-22)
[ES] La resolución de ecuaciones y sistemas no lineales es un tema de gran interés teórico-práctico, pues muchos modelos matemáticos de la ciencia o de la industria se expresan mediante sistemas no lineales o ecuaciones ...
[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 ...