Artidiello, Santiago; Cordero Barbero, Alicia; Torregrosa Sánchez, Juan Ramón; Vassileva, María P.(MDPI AG, 2020-01)
[EN] A secant-type method is designed for approximating the inverse and some generalized inverses of a complex matrix A. For a nonsingular matrix, the proposed method gives us an approximation of the inverse and, when the ...
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, ...
[EN] It is known that the concept of optimality is not defined for multidimensional iterative methods for solving nonlinear systems of equations. However, usually optimal fourth order schemes (extended to the case of several ...
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] The dynamical behavior of the rational vectorial operator associated with a multidimensional iterative method on polynomial systems gives us interesting information about the stability of the iterative scheme. The ...
[EN] In this paper we give a local convergence result for a uniparametric family of iterative methods for nonlinear equations in Banach spaces. We assume boundedness conditions involving only the first Fr,chet derivative, ...
Cordero Barbero, Alicia; Torregrosa Sánchez, Juan Ramón(Elsevier, 2015-02)
In this paper, a procedure to design Steffensen-type methods of different orders for solving nonlinear equations is suggested. By using a particular divided difference of first order we can transform many iterative methods ...
Cordero Barbero, Alicia; Franqués García, Antonio María; Torregrosa Sánchez, Juan Ramón(Springer, 2015-07-11)
[EN] In this paper, a parametric family of iterative methods for solving nonlinear systems, including Homeier’s scheme is presented, proving its third-order of convergence. The numerical section is devoted to obtain an ...
Cordero Barbero, Alicia; García-Maimo, Javier; Torregrosa Sánchez, Juan Ramón; Vassileva, Maria P.(Springer-Verlag, 2017)
[EN] In this paper, we present a multidimensional real dynamical study of the Ostrowsky-Chun family of iterative methods to solve systems of nonlinear equations. This family was defined initially for solving scalar equations ...
Cordero Barbero, Alicia; Ezquerro, J. A.; Hernández Verón, M. A.; Torregrosa Sánchez, Juan Ramón(Elsevier, 2015-01-15)
[EN] A new predictor–corrector iterative procedure, that combines Newton’s method as
predictor scheme and a fifth-order iterative method as a corrector, is designed for solving
nonlinear equations in Banach spaces. We ...
[EN] In this paper, a new technique to construct a family of divided differences for designing derivative-free iterative methods for solving nonlinear systems is proposed. By using these divided differences any kind of ...
Hueso Pagoaga, José Luís; Martínez Molada, Eulalia(Springer-Verlag, 2014)
[EN] In this work, we prove a third and fourth convergence order result for a family of iterative methods for solving nonlinear systems in Banach spaces. We analyze the semilocal convergence by using recurrence relations, ...
[EN] In this paper, a parametric family of seventh-order of iterative method to solve systems of nonlinear equations is presented. Its local convergence is studied and quadratic polynomials are used to investigate its ...
Amiri, A. R.; Cordero Barbero, Alicia; Darvishi, M. T.; Torregrosa Sánchez, Juan Ramón(Springer-Verlag, 2019-05)
[EN] The dynamical properties of a family of forward, central divided differences and Richardson extrapolation technique are studied. Applying these tools, an iterative method for solving nonlinear systems can be transformed ...
[EN] It is well known that scalar iterative methods with derivatives are highly more stable than their derivative-free partners, understanding the term stability as a measure of the wideness of the set of converging initial ...
Babajee, D.K.R.; Cordero Barbero, Alicia; Torregrosa Sánchez, Juan Ramón(Elsevier, 2016)
[EN] Many iterative methods for solving nonlinear equations have been developed recently. The main advantage claimed by their authors is the improvement of the order of convergence. In this work, we compare their dynamical ...
A new iterative method for polynomial root-finding based on the development of two novel recursive functions is proposed. In addition, the concept of polynomial pivots associated with these functions is introduced. The ...