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Listar por autor "Triguero Navarro, Paula"

Mostrando ítems 1-14 de 14

A General Optimal Iterative Scheme with Arbitrary Order of Convergence

Cordero Barbero, Alicia; Torregrosa Sánchez, Juan Ramón; Triguero-Navarro, Paula (MDPI AG, 2021-05)

[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, ...
An iterative scheme to obtain multiple solutions simultaneously

Cordero Barbero, Alicia; Garrido-Saez, Neus; Torregrosa Sánchez, Juan Ramón; Triguero-Navarro, Paula (Elsevier, 2023-11)

[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 ...
Convergence and Stability of a Parametric Class of Iterative Schemes for Solving Nonlinear Systems

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 ...
Design of iterative methods with memory for solving nonlinear systems

Cordero Barbero, Alicia; Garrido-Saez, Neus; Torregrosa Sánchez, Juan Ramón; Triguero-Navarro, Paula (John Wiley & Sons, 2023-08)

[EN] In this paper, we design two parametric classes of iterative methods without memory to solve nonlinear systems, whose convergence order is 4 and 7, respectively. From their error equations and to increase the convergence ...
Efficient parametric family of fourth-order Jacobian-free iterative vectorial schemes

Cordero Barbero, Alicia; Rojas-Hiciano, Renso V.; Torregrosa Sánchez, Juan Ramón; Triguero-Navarro, Paula (Springer-Verlag, 2024)

[EN] In this work, a multiparametric family of iterative vectorial fourth-order methods free of Jacobian matrices is proposed. A convergence analysis of this family is carried out as well as a study of its efficiency. ...
High Performance Multidimensional Iterative Processes for Solving Nonlinear Equations

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 ...
Introducing memory to a family of multi-step multidimensional iterative methods with weight function

Cordero Barbero, Alicia; Villalba, Eva G.; Torregrosa Sánchez, Juan Ramón; Triguero-Navarro, Paula (Elsevier GmbH, 2023-06)

[EN] In this paper, we construct a derivative-free multi-step iterative scheme based on Steffensen's method. To avoid excessively increasing the number of functional evaluations and, at the same time, to increase the order ...
Iterative schemes for finding all roots simultaneously of nonlinear equations

Cordero Barbero, Alicia; Garrido-Saez, Neus; Torregrosa Sánchez, Juan Ramón; Triguero-Navarro, Paula (Elsevier, 2022-12)

[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 ...
Memory in the iterative processes for nonlinear problems

Cordero Barbero, Alicia; Garrido-Saez, Neus; Torregrosa Sánchez, Juan Ramón; Triguero-Navarro, Paula (John Wiley & Sons, 2023-03-15)

[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 ...
Modifying Kurchatov's method to find multiple roots

Cordero Barbero, Alicia; Garrido-Saez, Neus; Torregrosa Sánchez, Juan Ramón; Triguero-Navarro, Paula (Universitat Politècnica de València, 2022-07-15)
Modifying Kurchatov's method to find multiple roots of nonlinear equations

Cordero Barbero, Alicia; Garrido-Saez, Neus; Torregrosa Sánchez, Juan Ramón; Triguero-Navarro, Paula (Elsevier, 2024-04)

[EN] We present a modification of Kurchatov's iterative method in order to solve a nonlinear equation with multiple roots, that is, for approximating solutions with multiplicity greater than one. One of its principal ...
Simultaneous roots for vectorial problems

Chinesta, Francisco; Cordero Barbero, Alicia; Garrido-Saez, Neus; Torregrosa Sánchez, Juan Ramón; Triguero-Navarro, Paula (Springer-Verlag, 2023-07)

[EN] In this manuscript, we design an iterative step that can be added to any numerical process for solving systems of nonlinear equations. By means of this addition, the resulting iterative scheme obtains, simultaneously, ...
Symmetry in the Multidimensional Dynamical Analysis of Iterative Methods with Memory

Cordero Barbero, Alicia; Garrido-Saez, Neus; Torregrosa Sánchez, Juan Ramón; Triguero-Navarro, Paula (MDPI AG, 2022-03)

[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 ...
Three-step iterative weight function scheme with memory for solving nonlinear problems

Cordero Barbero, Alicia; Garrido-Saez, Neus; Torregrosa Sánchez, Juan Ramón; Triguero-Navarro, Paula (John Wiley & Sons, 2023-07)

[EN] In this manuscript, we present a parametric family of derivative-free three-step iterative methods with a weight function for solving nonlinear equations. We study various ways of introducing memory to this parametric ...