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 ...
Hernández-Verón, Miguel Angel; Martínez Molada, Eulalia(Elsevier, 2018)
[EN] Solving equations of the form H(x) = 0 is usually done by applying iterative methods. The main interest of this paper is to improve the domain of starting points for Steffensen's method. In general, the accessibility ...
[EN] In this paper, we establish a qualitative study of nonlinear Fredholm integral equations, where we will carry out a study on the localization and separation of solutions. Moreover, we consider an efficient algorithm ...
[EN] This paper is devoted to the construction and analysis of an efficient k-step iterative method for nonlinear equations. The main advantage of this method is that it does not need to evaluate any high order Frechet ...
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 ...
Hernández-Verón, Miguel Angel; Martínez Molada, Eulalia; Teruel-Ferragud, Carles(Springer-Verlag, 2017)
[EN] In this paper, we analyze the semilocal convergence of k-steps Newton's method with frozen first derivative in Banach spaces. The method reaches order of convergence k + 1. By imposing only the assumption that the ...