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 ...
[EN] A general optimal iterative method, for approximating the solution of nonlinear equations, of (n+1) steps with 2(n+1) order of convergence is presented. Cases n=0 and n=1 correspond to Newton's and Ostrowski's schemes, ...
Behl, Ramandeep; Cordero Barbero, Alicia; Torregrosa Sánchez, Juan Ramón(Elsevier, 2022-04)
[EN] In this paper, we presented a novel and efficient fourth order derivative free optimal family of iterative methods for approximating the multiple roots of nonlinear equations. Initially the convergence analysis is ...
[EN] In this paper, we present a new third-order family of iterative methods in order to compute the multiple roots of nonlinear equations when the multiplicity (m >= 1) is known in advance. There is a plethora of third-order ...
A new two-parametric family of derivative-free iterative methods for solving nonlinear equations is presented. First, a new biparametric family without memory of optimal order four is proposed. The improvement of the ...
Chicharro, Francisco I.; Cordero Barbero, Alicia; Garrido, Neus; Torregrosa Sánchez, Juan Ramón(John Wiley & Sons, 2020-01-12)
[EN] The stability analysis of a new family of iterative methods with memory is introduced. This family, designed from Traub's method, allows to add memory through the introduction of an accelerating parameter. Hence, the ...
Cordero Barbero, Alicia; Guasp, Lucia; Torregrosa Sánchez, Juan Ramón(Elsevier, 2018)
[EN] In this manuscript, we analyze the dynamical anomalies of a parametric family of iterative schemes designed by Kou et al. It is known that its order of convergence is three for any arbitrary value of the parameter, ...
Chicharro López, Francisco Israel; Cordero Barbero, Alicia; Gutiérrez, José M.; Torregrosa Sánchez, Juan Ramón(Elsevier, 2013-02-15)
The dynamical behavior of two iterative derivative-free schemes, Steffensen and M4 methods, is studied in case of quadratic and cubic polynomials. The parameter plane is analyzed for both procedures on quadratic polynomials. ...
Campos, Beatriz; Cordero Barbero, Alicia; Torregrosa Sánchez, Juan Ramón; Vindel, Pura(American Institute of Mathematical Sciences, 2022)
[EN] Qualitative analysis of iterative methods with memory has been carried out a few years ago. Most of the papers published in this context analyze the behaviour of schemes on quadratic polynomials. In this paper, we ...
[EN] In this manuscript, by using the weight-function technique, a new class of iterative methods for solving nonlinear problems is constructed, which includes many known schemes that can be obtained by choosing different ...
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 ...
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] 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; Jordan-Lluch, Cristina; Torregrosa Sánchez, Juan Ramón(Elsevier, 2015-02)
In this paper, a unified point of view that includes the most of one-point Newton-type iterative
methods for solving nonlinear equations is introduced. A simple idea to design iterative
methods with quadratic or cubic ...
In this paper, by using a generalization of Ostrowski' and Chun's methods two bi-parametric families of predictor-corrector iterative schemes, with order of convergence four for solving system of nonlinear equations, are ...
Chicharro, Francisco I.; Cordero Barbero, Alicia; Garrido, Neus; Torregrosa Sánchez, Juan Ramón(Springer-Verlag, 2019-05)
[EN] Based on the third-order Traub's method, two iterative schemes with memory are introduced. The proper inclusion of accelerating parameters allows the introduction of memory. Therefore, the order of convergence of the ...
[EN] In this manuscript, we present a parametric family of derivative-free three-step iterative methods with a weight function for solving nonlinear equations. We study various ways of introducing memory to this parametric ...
Two new three-step classes of optimal iterative methods to approximate simple roots of nonlinear equations, satisfying the Kung-Traub's conjecture, are designed. The development of the methods and their convergence analysis ...
Artidiello Moreno, Santiago de Jesús; Cordero Barbero, Alicia; Torregrosa Sánchez, Juan Ramón; Vassileva, M.P.(Taylor & Francis: STM, Behavioural Science and Public Health Titles, 2015-09-02)
In this paper we design, by using the weight function technique, two families of iterative schemes with order of convergence eight. These weight functions depend on one, two and three variables and they are used in the ...