[EN] In this manuscript, a new family of Jacobian-free iterative methods for solving nonlinear systems is presented. The fourth-order convergence for all the elements of the class is established, proving, in addition, that ...
[EN] In this manuscript, we propose a new highly efficient and optimal scheme of order sixteen for obtaining simple roots of nonlinear equations. The derivation of this scheme is based on the rational approximation approach. ...
Chicharro, Francisco I.; Cordero Barbero, Alicia; Garrido-Saez, Neus; Torregrosa Sánchez, Juan Ramón(Taylor & Francis, 2019-10-03)
[EN] A bi-parametric family of iterative schemes for solving nonlinear systems is presented. We prove for any value of parameters the sixth-order of convergence of any members of the class. The efficiency and computational ...
Budzko, Dzmitry; Cordero Barbero, Alicia; Torregrosa Sánchez, Juan Ramón(Elsevier, 2015-02-01)
[EN] A new parametric class of third-order iterative methods for solving nonlinear equations
and systems is presented. These schemes are showed to be more stable than Newton’,
Traub’ or Ostrowski’s procedures (in some ...
In this manuscript, a new parametric class of iterative methods for solving nonlinear systems of equations is proposed. Its fourth-order of convergence is proved and a dynamical analysis on low-degree polynomials is made ...
[EN] We used a Kurchatov-type accelerator to construct an iterative method with memory for solving nonlinear systems, with sixth-order convergence. It was developed from an initial scheme without memory, with order of ...
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 ...
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 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 ...
[EN] In this work, a new class of iterative methods for solving nonlinear equations is presented and also its extension for nonlinear systems of equations. This family is developed by using a scalar and matrix weight ...
[EN] In this paper, we propose a general bi-parametric family of sixth order iterative methods to solve systems of nonlinear equations. The presented scheme contains some well known existing methods as special cases. The ...
Cordero Barbero, Alicia; Torregrosa Sánchez, Juan Ramón(Elsevier, 2017)
[EN] A new iterative method for computing the polar decomposition of any rectangular complex matrix is presented and analyzed. The study of the convergence shows that this method has order of convergence six. Some numerical ...
[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 ...
Kansal, Munish; Cordero Barbero, Alicia; Torregrosa Sánchez, Juan Ramón; Bhalla, Sonia(Walter de Gruyter GmbH, 2020-10)
[EN] There have appeared in the literature a lot of optimal eighth-order iterative methods for approximating simple zeros of nonlinear functions. Although, the similar ideas can be extended for the case of multiple zeros ...
[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 ...
[EN] In this manuscript, we propose several iterative methods for solving nonlinear equations whose common origin is the classical Chebyshev's method, using fractional derivatives in their iterative expressions. Due to the ...
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] Finding a repeated zero for a nonlinear equation f(x) = 0, f : I subset of R -> R has always been of much interest and attention due to its wide applications in many fields of science and engineering. Modified Newton's ...