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Open AccessArticle

Expanding the Applicability of a Third Order Newton-Type Method Free of Bilinear Operators

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Departamento de Matemática Aplicada y Estadística, Universidad de Cartagena,Cartagena 21833, Spain
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Escuela de Ingeniería, Universidad Internacional de La Rioja, C/Gran Vía 41, Logroño (La Rioja) 26005, Spain
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Author to whom correspondence should be addressed.
Academic Editor: Alicia Cordero
Algorithms 2015, 8(3), 669-679; https://doi.org/10.3390/a8030669
Received: 26 May 2015 / Revised: 9 August 2015 / Accepted: 14 August 2015 / Published: 21 August 2015
(This article belongs to the Special Issue Numerical Algorithms for Solving Nonlinear Equations and Systems)
This paper is devoted to the semilocal convergence, using centered hypotheses, of a third order Newton-type method in a Banach space setting. The method is free of bilinear operators and then interesting for the solution of systems of equations. Without imposing any type of Fréchet differentiability on the operator, a variant using divided differences is also analyzed. A variant of the method using only divided differences is also presented. View Full-Text
Keywords: Newton type methods; third order; semilocal convergence; centered hypotheses; divided differences Newton type methods; third order; semilocal convergence; centered hypotheses; divided differences
MDPI and ACS Style

Amat, S.; Busquier, S.; Bermúdez, C.; Magreñán, Á.A. Expanding the Applicability of a Third Order Newton-Type Method Free of Bilinear Operators. Algorithms 2015, 8, 669-679.

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