Dynamics and local convergence of a family of derivative-free iterative processes

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:354

Article; Proceedings Paper

Hernandez-Veron, M. A.¹  Magrenan, A. A.¹  Rubio, M. J.¹ 

[1] Univ La Rioja, Complejo Cient Tecnoloog, Dept Math & Computat, Calle Madre Dios 53, Logrono 26006, Spain

关键词: Iterative processes;    Steffensen method;    Local convergence;    Iterative processes derivative -free;    Divided differences;   

DOI  :  10.1016/j.cam.2018.08.032

来源: Elsevier

【 摘 要 】

In this paper we establish the construction of a family of free derivative of point to point iterative processes, with quadratic convergence, from two known data in each previous iteration. Besides, we study the accessibility of this family by means of the basins of attraction and the convergence balls. We provide a local convergence analysis for the family of iterative processes free of derivatives, when the operator F is not necessarily Frechet differentiable. The sufficient convergence conditions are weaker and more flexible than in earlier studies. An application is provided involving mixed Hammerstein nonlinear integral equation with application in real world problems. Finally, we show also a dynamical study and the convergence regions of some members of the family. (C) 2018 Elsevier B.V. All rights reserved.

【 授权许可】

Free