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Algorithms 2017, 10(2), 64; doi:10.3390/a10020064

Expanding the Applicability of Some High Order Househölder-Like Methods

1
Departamento de Matemática Aplicada y Estadística, Universidad Politécnica de Cartagena, Cartagena 30203, Spain
2
Department of Mathematics Sciences, Cameron University, Lawton, OK 73505, USA
3
Departamento de Matemáticas y Computación, Universidad de La Rioja, Logroño 26004, Spain
*
Author to whom correspondence should be addressed.
Academic Editors: Alicia Cordero, Juan R. Torregrosa and Francisco I. Chicharro
Received: 3 April 2017 / Revised: 26 May 2017 / Accepted: 26 May 2017 / Published: 31 May 2017
(This article belongs to the Special Issue Numerical Algorithms for Solving Nonlinear Equations and Systems 2017)
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Abstract

This paper is devoted to the semilocal convergence of a Househölder-like method for nonlinear equations. The method includes many of the studied third order iterative methods. In the present study, we use our new idea of restricted convergence domains leading to smaller γ -parameters, which in turn lead to the following advantages over earlier works (and under the same computational cost): larger convergence domain; tighter error bounds on the distances involved, and at least as precise information on the location of the solution. View Full-Text
Keywords: Househölder-like methods; nonlinear systems of equations; Banach space; semilocal convergence; γ-like conditions Househölder-like methods; nonlinear systems of equations; Banach space; semilocal convergence; γ-like conditions
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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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MDPI and ACS Style

Amat, S.; Argyros, I.K.; Hernández-Verón, M.A.; Romero, N. Expanding the Applicability of Some High Order Househölder-Like Methods. Algorithms 2017, 10, 64.

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