Amat, Sergio; Argyros, Ioannis K.; Busquier, Sonia; Hernández-Verón, Miguel Angel; Magreñán, A. Alberto; Martínez Molada, Eulalia(John Wiley & Sons, 2020-06-15)
[EN] This paper is devoted to the semilocal analysis of a high-order Steffensen-type method with frozen divided differences. The methods are free of bilinear operators and derivatives, which constitutes the main limitation ...
[EN] The objective in this paper is the expansion of the utilization for a fifth convergence order scheme without derivatives for finding solutions of Banach space valued equations. Conditions of the first order divided ...
Argyros, Ioannis K.; Cordero Barbero, Alicia; Magreñán Ruiz, Ángel Alberto; Torregrosa Sánchez, Juan Ramón(Elsevier, 2015-09-01)
[EN] We present a convergence analysis for a damped Newton-like method with modified righthand
side vector in order to approximate a locally unique solution of a nonlinear equation in
a Banach spaces setting. In the ...
Argyros, Ioannis K.; Cordero Barbero, Alicia; Magreñán Ruiz, Ángel Alberto; Torregrosa Sánchez, Juan Ramón(Elsevier, 2015-02-01)
[EN] We present a convergence analysis for a Damped Secant method with modified right-hand
side vector in order to approximate a locally unique solution of a nonlinear equation in a
Banach spaces setting. In the special ...
Argyros, Ioannis K.; Cordero Barbero, Alicia; Alberto Magreñán, A.; Torregrosa Sánchez, Juan Ramón(Elsevier, 2017)
[EN] In this paper, we present the study of the local convergence of a higher-order family of methods. Moreover, the dynamical behavior of this family of iterative methods applied to quadratic polynomials is studied. Some ...
Amat, Sergio; Argyros, Ioannis K.; Busquier Saez, Sonia; Hernández-Verón, Miguel Angel; Martínez Molada, Eulalia(Elsevier, 2018-12-01)
[EN] This paper is devoted to a family of Newton-like methods with frozen derivatives used to approximate a locally unique solution of an equation. The methods have high order of convergence but only using first order ...
Argyros, Ioannis K.; Cordero Barbero, Alicia; Alberto Magreñán, A.; Torregrosa Sánchez, Juan Ramón(Elsevier, 2017)
[EN] Traub's method is a tough competitor of Newton's scheme for solving nonlinear equations as well as nonlinear systems. Due to its third-order convergence and its low computational cost, it is a good procedure to be ...