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

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...

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Bibliographic Details
Published in:Algorithms 2015-09, Vol.8 (3), p.669-679
Main Authors: Amat, Sergio, Busquier, Sonia, Bermúdez, Concepción, Magreñán, Ángel
Format: Article
Language:English
Subjects:
Algorithms
Banach space
centered hypotheses
Convergence
divided differences
Hypotheses
Mathematical analysis
Newton type methods
Operators
semilocal convergence
third order
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Summary: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.
ISSN:1999-4893
1999-4893
DOI:10.3390/a8030669