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Algorithms 2015, 8(3), 669-679; doi:10.3390/a8030669

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

1
Departamento de Matemática Aplicada y Estadística, Universidad de Cartagena,Cartagena 21833, Spain
2
Escuela de Ingeniería, Universidad Internacional de La Rioja, C/Gran Vía 41, Logroño (La Rioja) 26005, Spain
*
Author to whom correspondence should be addressed.
Academic Editor: Alicia Cordero
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)
View Full-Text   |   Download PDF [212 KB, uploaded 21 August 2015]

Abstract

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
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.; 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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