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 ...
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. ...
In this paper we present an infinite family of one-step iterative formulas for solving nonlinear equations (Present Method One), from now on PMI, that can be expressed as xn+1=Fm(xn), with 1<= m<= infinite, integer, Fm ...
Cordero Barbero, Alicia; Maimo, Javier G.; Rodríguez-Cabral, Antmel; Torregrosa Sánchez, Juan Ramón(MDPI AG, 2023-03)
[EN] In this manuscript, we carry out a study on the generalization of a known family of multipoint scalar iterative processes for approximating the solutions of nonlinear systems. The convergence analysis of the proposed ...
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 ...
Hueso Pagoaga, José Luís; Martínez Molada, Eulalia; Teruel, Carles(Elsevier, 2015-05-15)
[EN] In this work we introduce a new operator of divided differences that preserves the convergence
order when it is used for approximating the Jacobian matrix in iterative method for
solving nonlinear systems. We obtain ...
[EN] In this work we focus on the problem of approximating multiple roots of nonlinear equations. Multiple roots appear in some applications such as the compression of band-limited signals and the multipactor effect in ...
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 ...
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 ...
[EN] In the recent literature, very few high-order Jacobian-free methods with memory for solving nonlinear systems appear. In this paper, we introduce a new variant of King's family with order four to solve nonlinear systems ...
In this paper we present and analyze a set of predictor-corrector iterative methods with increasing order of convergence, for solving systems of nonlinear equations. Our aim is to achieve high order of convergence with few ...
[EN] This study is devoted to solve the Chandrasekhar integral equation that it is used for modeling problems in theory of radiative transfer in a plane-parallel atmosphere, and others research areas like the kinetic theory ...
Cordero Barbero, Alicia; Torregrosa Sánchez, Juan Ramón; Vassileva, María P.(Elsevier, 2012-08-01)
A new technique for designing iterative methods for solving nonlinear systems is presented. This procedure, called pseudocomposition, uses a known method as a predictor and the Gaussian quadrature as a corrector. The order ...
Cordero Barbero, Alicia; Ramos, Higinio; Torregrosa Sánchez, Juan Ramón(Springer-Verlag, 2020-04)
[EN] In this paper, we develop some variants of the well-known Halley's iterative method to solve nonlinear equations. The resulting methods are one-step methods, with and without memory, which use different number of ...
Cordero Barbero, Alicia; Hueso Pagoaga, José Luís; Martínez Molada, Eulalia; Torregrosa Sánchez, Juan Ramón(Elsevier, 2012-06)
[EN] In the present paper, by approximating the derivatives in the well known fourth-order Ostrowski's method and in a sixth-order improved Ostrowski's method by central-difference quotients, we obtain new modifications ...
In this paper, based on Ostrowski's method, a new family of eighth-order methods for solving nonlinear equations is derived. In terms of computational cost, each iteration of these methods requires three evaluations of the ...