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Mostrando ítems 1-20 de 44

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A class of optimal eighth-order derivative-free methods for solving the Danchick-Gauss problem

Andreu Estellés, Carlos; Cambil Teba, Noelia; Cordero Barbero, Alicia; Torregrosa Sánchez, Juan Ramón (Elsevier, 2014-04-01)

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 ...
A convex combination approach for mean-based variants of Newton's method

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 ...
A dynamical comparison between iterative methods with memory: Are the derivatives good for the memory?

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 ...
A general class of four parametric with and without memory iterative methods for nonlinear equations

Zafar, Fiza; Cordero Barbero, Alicia; Torregrosa Sánchez, Juan Ramón; Rafi, Aneeqa (Springer-Verlag, 2019-05)

[EN] In this paper, we have constructed a derivative-free weighted eighth-order iterative class of methods with and without-memory for solving nonlinear equations. These methods are optimal as they satisfy Kung-Traub's ...
A General Optimal Iterative Scheme with Arbitrary Order of Convergence

Cordero Barbero, Alicia; Torregrosa Sánchez, Juan Ramón; Triguero-Navarro, Paula (MDPI AG, 2021-05)

[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, ...
A multidimensional dynamical approach to iterative methods with memory

Campos, Beatriz; Cordero Barbero, Alicia; Torregrosa Sánchez, Juan Ramón; Vindel, Pura (Elsevier, 2015-11-15)

[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 ...
A new efficient and optimal sixteenth-order scheme for simple roots of nonlinear equations

Behl, Ramandeep; Cordero Barbero, Alicia; Motsa, Sandile S.; Torregrosa Sánchez, Juan Ramón (2017)

[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. ...
A new family of iterative methods widening areas of convergence

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 ...
A stable family with high order of convergence for solving nonlinear equations

Cordero Barbero, Alicia; Lotfi, Taher; Mahdiani, Katayoun; Torregrosa Sánchez, Juan Ramón (Elsevier, 2015-03-01)

[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 ...
A Variant of Chebyshev's Method with 3 alpha th-Order of Convergence by Using Fractional Derivatives

Cordero Barbero, Alicia; Girona, Ivan; Torregrosa Sánchez, Juan Ramón (MDPI AG, 2019-08-06)

[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 ...
Accelerated iterative methods for finding solutions of nonlinear equations and their dynamical behavior

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. ...
An efficient Steffensen-like iterative method with memory

Cordero Barbero, Alicia; Lotfi, T.; Khoshandi, A.; Torregrosa Sánchez, Juan Ramón (Société des Sciences Mathématiques de Roumanie, 2015)

[EN] Some methods with memory for solving nonlinear equations are designed from known methods without memory. We increase the convergence order from 4 to 6 by using a free parameter accelerator by Newton's interpolatory ...
An optimal eighth order derivative free multiple root finding numerical method and applications to chemistry

Cordero Barbero, Alicia; Fiza Zafar; Ifra Ashraf; Torregrosa Sánchez, Juan Ramón (Springer-Verlag, 2023-01)

[EN] In this paper, we present an optimal eighth order derivative-free family of methods for multiple roots which is based on the first order divided difference and weight functions. This iterative method is a three step ...
An optimal fourth-order family of methods for multiple roots and its dynamics

Behl, Ramandeep; Cordero Barbero, Alicia; Motsa, Sandile S.; Torregrosa Sánchez, Juan Ramón; Kanwar, Vinay (Springer-Verlag, 2016)

[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 ...
Anomalies in the convergence of Traub-type methods with memory

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 ...
Choosing the most stable members of Kou's family of iterative methods

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, ...
CMMSE-2019 mean-based iterative methods for solving nonlinear chemistry problems

Chicharro, Francisco I.; Cordero Barbero, Alicia; Martínez, Tobías H.; Torregrosa Sánchez, Juan Ramón (Springer-Verlag, 2020-03)

[EN] The third-order iterative method designed by Weerakoon and Fernando includes the arithmetic mean of two functional evaluations in its expression. Replacing this arithmetic mean with different means, other iterative ...
Construction of fourth-order optimal families of iterative methods and their dynamics

Behl, Ramandeep; Cordero Barbero, Alicia; Motsa, Sandile S.; Torregrosa Sánchez, Juan Ramón (Elsevier, 2015-11-15)

[EN] In this paper, we propose a general class of fourth-order optimal multi-point methods without memory for obtaining simple roots. This class requires only three functional evaluations (viz. two evaluations of function ...
Design and Complex Dynamics of Potra-Pták-Type Optimal Methods for Solving Nonlinear Equations and Its Applications

Chand, Prem B.; Chicharro, Francisco I.; Garrido Saez, Neus; Jain, Pankaj (MDPI AG, 2019-10)

[EN] In this paper, using the idea of weight functions on the Potra¿Pták method, an optimal fourth order method, a non optimal sixth order method, and a family of optimal eighth order methods are proposed. These methods ...
Dynamical analysis of iterative methods for nonlinear systems or how to deal with the dimension?

Cordero Barbero, Alicia; Soleymani, Fazlollah; Torregrosa Sánchez, Juan Ramón (Elsevier, 2014-10-01)

This paper deals with the real dynamical analysis of iterative methods for solving nonlinear systems on vectorial quadratic polynomials. We use the extended concept of critical point and propose an easy test to determine ...