A derivative-free optimal eighth-order family of iterative methods for solving nonlinear equations is constructed using weight functions approach with divided first order differences. Its performance, along with several ...
Cordero Barbero, Alicia; Torregrosa Sánchez, Juan Ramón(Elsevier, 2011-06-01)
In this paper, a family of Steffensen type methods of fourth-order convergence for solving nonlinear smooth equations is suggested. In the proposed methods, a linear combination of divided differences is used to get a ...
Cordero Barbero, Alicia; Torregrosa Sánchez, Juan Ramón; Vassileva, María Penkova(Elsevier, 2011-12)
In this paper, we derive a new family of eighth-order methods for obtaining simple roots of nonlinear equations by using the weight function method. Each iteration of these methods requires three evaluations of the function ...
Cordero Barbero, Alicia; Hueso Pagoaga, José Luís; Martínez Molada, Eulalia; Torregrosa Sánchez, Juan Ramón(Elsevier, 2013-11)
A new technique to obtain derivative-free methods with optimal order of convergence in the sense of the Kung-Traub conjecture for solving nonlinear smooth equations is described. The procedure uses Steffensen-like methods ...
[EN] In this paper, we present a uniparametric family of modified Chebyshev-Halley type methods with optimal eighth-order of convergence. In terms of computational cost, each member of the family requires only four functional ...
[EN] Recently, Li et al. (2014) have published a new family of iterative methods, without memory,
with order of convergence five or six, which are not optimal in the sense of Kung and
Traub’s conjecture. Therefore, we ...
Cordero Barbero, Alicia; Fardi, M.; Ghasemi, M.; Torregrosa Sánchez, Juan Ramón(Springer Verlag (Germany), 2014-03)
In this paper, we present a family of optimal, in the sense of Kung-Traub's conjecture, iterative methods for solving nonlinear equations with eighth-order convergence. Our methods are based on Chun's fourth-order method. ...
[EN] There is a very small number of higher-order iteration functions for multiple zeros whose order of convergence is greater than four. Some scholars have tried to propose optimal eighth-order methods for multiple zeros. ...
In this paper the problem of the determination of the preliminary orbit of a celestial body is studied. We compare the results obtained by the classical Gauss's method with those obtained by some higher-order iterative ...
Arroyo Martínez, Víctor; Cordero Barbero, Alicia; Torregrosa Sánchez, Juan Ramón; Penkova Vassileva, María(Taylor & Francis Ltd, 2012)
In recent years, high-order methods have shown to be very useful in many practical applications, in which nonlinear systems arise. In this case, a classical method of positional astronomy have been modified in order to ...
Hueso Pagoaga, José Luís; Martínez Molada, Eulalia; Teruel, Carles(Elsevier, 2015-02)
[EN] In this work we present a new family of iterative methods for solving nonlinear systems
that are optimal in the sense of Kung and Traub’s conjecture for the unidimensional case.
We generalize this family by performing ...
Chicharro López, Francisco Israel; Cordero Barbero, Alicia; Torregrosa Sánchez, Juan Ramón(Elsevier, 2013-04)
From position and velocity coordinates for several given instants, it is possible to determine the orbital elements of the preliminary orbit, taking only into account mutual gravitational attraction forces between the Earth ...
Artidiello, S.; Cordero Barbero, Alicia; Torregrosa Sánchez, Juan Ramón; Vassileva, M. P.(Elsevier, 2017)
[EN] In this paper, a three-step iterative method with sixth-order local convergence for approximating the solution of a nonlinear system is presented. From Ostrowski¿s scheme adding one step of Newton with ¿frozen¿ ...
Cordero Barbero, Alicia; Hueso Pagoaga, José Luís; Martínez Molada, Eulalia; Torregrosa Sánchez, Juan Ramón(Elsevier, 2011-01-01)
We derive new iterative methods with order of convergence four or higher, for solving nonlinear systems, by composing iteratively golden ratio methods with a modified Newton's method. We use different efficiency indices ...
Cordero Barbero, Alicia; Hueso Pagoaga, José Luís; Martínez Molada, Eulalia; Torregrosa Sánchez, Juan Ramón(Elsevier, 2013-04)
In this work we show a general procedure to obtain optimal derivative free iterative methods for nonlinear equations f (x) = 0, applying polynomial interpolation to a generic optimal derivative free iterative method of ...
[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 ...
Cordero Barbero, Alicia; Hueso Pagoaga, José Luís; Martínez Molada, Eulalia; Torregrosa Sánchez, Juan Ramón(Elsevier, 2012-12)
In this work we introduce a technique for solving nonlinear systems that improves the order of convergence of any given iterative method which uses the Newton iteration as a predictor. The main idea is to compose a given ...
[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; 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 ...
En esta memoria se presentan dos métodos iterativos de órdenes cuatro y cinco, respectivamente, para resolver sistemas no lineales de ecuaciones. Realizamos comparaciones numéricas con otros métodos existente de órdenes ...