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Algorithms 2015, 8(4), 1121-1128; doi:10.3390/a8041121

On the Local Convergence of a Third Order Family of Iterative Processes

Department of Mathematics and Computation, University of La Rioja, Calle Luis de Ulloa s/n, Logroño, Spain
These authors contributed equally to this work.
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Academic Editor: Alicia Cordero
Received: 7 September 2015 / Revised: 24 November 2015 / Accepted: 26 November 2015 / Published: 1 December 2015
(This article belongs to the Special Issue Numerical Algorithms for Solving Nonlinear Equations and Systems)
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Abstract

Efficiency is generally the most important aspect to take into account when choosing an iterative method to approximate a solution of an equation, but is not the only aspect to consider in the iterative process. Another important aspect to consider is the accessibility of the iterative process, which shows the domain of starting points from which the iterative process converges to a solution of the equation. So, we consider a family of iterative processes with a higher efficiency index than Newton’s method. However, this family of proecsses presents problems of accessibility to the solution x * . From a local study of the convergence of this family, we perform an optimization study of the accessibility and obtain iterative processes with better accessibility than Newton’s method. View Full-Text
Keywords: nonlinear equation; iterative method; local convergence; accessibility of solution; Newton’s method nonlinear equation; iterative method; local convergence; accessibility of solution; Newton’s method
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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Hernández-Verón, M.A.; Romero, N. On the Local Convergence of a Third Order Family of Iterative Processes. Algorithms 2015, 8, 1121-1128.

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