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Browsing by Subject "Divided difference"

Now showing items 1-7 of 7

A class of Steffensen type methods with optimal order of convergente

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 ...
Extended convergence for a fifth-order novel scheme free from derivatives

Behl, Ramandeep; Argyros, Ioannis K.; Martínez Molada, Eulalia; Joshi, Janak (John Wiley & Sons, 2022-04)

[EN] The objective in this paper is the expansion of the utilization for a fifth convergence order scheme without derivatives for finding solutions of Banach space valued equations. Conditions of the first order divided ...
Low-complexity root-finding iteration functions with no derivatives of any order of convergence

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 ...
Memory in the iterative processes for nonlinear problems

Cordero Barbero, Alicia; Garrido-Saez, Neus; Torregrosa Sánchez, Juan Ramón; Triguero-Navarro, Paula (John Wiley & Sons, 2023-03-15)

[EN] In this paper, we study different ways for introducing memory to a parametric family of optimal two-step iterative methods. We study the convergence and the stability, by means of real dynamics, of the methods obtained ...
Preserving the order of convergence: Low-complexity Jacobian-free iterative schemes for solving nonlinear systems

Amiri, Abdolreza; Cordero Barbero, Alicia; Darvishi, M.T.; Torregrosa Sánchez, Juan Ramón (Elsevier, 2018-08-01)

[EN] In this paper, a new technique to construct a family of divided differences for designing derivative-free iterative methods for solving nonlinear systems is proposed. By using these divided differences any kind of ...
Semilocal Convergence of the Extension of Chun's Method

Cordero Barbero, Alicia; Maimó, Javier G.; Martínez Molada, Eulalia; Torregrosa Sánchez, Juan Ramón; Vassileva, Maria P. (MDPI AG, 2021-09)

[EN] In this work, we use the technique of recurrence relations to prove the semilocal convergence in Banach spaces of the multidimensional extension of Chun's iterative method. This is an iterative method of fourth order, ...
Stability analysis of Jacobian-free iterative methods for solving nonlinear systems by using families of mth power divided differences

Amiri, A. R.; Cordero Barbero, Alicia; Darvishi, M. T.; Torregrosa Sánchez, Juan Ramón (Springer-Verlag, 2019-05)

[EN] The dynamical properties of a family of forward, central divided differences and Richardson extrapolation technique are studied. Applying these tools, an iterative method for solving nonlinear systems can be transformed ...