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 ...
Company Rossi, Rafael; Jódar Sánchez, Lucas Antonio; Pintos Taronger, José Ramón(Elsevier, 2012-06)
Markets liquidity is an issue of very high concern in financial risk management. In a perfect liquid market the option pricing model becomes the well-known linear Black-Scholes problem. Nonlinear models appear when transaction ...
Cordero Barbero, Alicia; Franceschi, Jonathan; Torregrosa Sánchez, Juan Ramón; Zagati, Anna C.(MDPI AG, 2019-09-02)
[EN] Several authors have designed variants of Newton¿s method for solving nonlinear equations by using different means. This technique involves a symmetry in the corresponding fixed-point operator. In this paper, some ...
Cordero Barbero, Alicia; Jordan-Lluch, Cristina; Torregrosa Sánchez, Juan Ramón(Elsevier, 2017)
[EN] The role of the derivatives at the iterative expression of methods with memory for solving nonlinear equations is analyzed in this manuscript. To get this aim, a known class of methods without memory is transformed ...
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 ...
Akgül, Alí; Cordero Barbero, Alicia; Torregrosa Sánchez, Juan Ramón(Elsevier, 2019-12)
[EN] The use of fractional calculus in many branches of Science and Engineering is wide in the last years. There are different kinds of derivatives that can be useful in different problems. In this manuscript, we put the ...
[EN] The aim of this paper is to introduce new high order iterative methods for multiple roots of the nonlinear scalar equation; this is a demanding task in the area of computational mathematics and numerical analysis. ...
Almenar, P.; Jódar Sánchez, Lucas Antonio(Elsevier, 2011-04)
This paper presents a Lyapunov-type inequality for the second order nonlinear equation (r(x)y')' + p(x)f(y(x)) = 0, with r(x), p(x) > 0 and f(y) odd and positive for y > O. It also compares it with similar results. (C) ...
[EN] A dynamical approach on the dynamics of iterative methods with memory for solving nonlinear
equations is made. We have designed new methods with memory from Steffensen’ or
Traub’s schemes, as well as from a parametric ...
[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. ...
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 revise the proofs of the results obtained in "Convergence radius of Osada's method under Holder continuous condition"[4], because the remainder of the Taylor's expansion used for the obtainment of the ...
[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 ...
[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 ...
[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 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 ...
[EN] There are few optimal fourth-order methods for solving nonlinear equations when the multiplicity m of the required root is known in advance. Therefore, the principle focus of this paper is on developing a new fourth-order ...