On the semilocal convergence of Newton-type methods, when the derivative is not continuously invertible

We provide a semilocal convergence analysis for Newton-type methods to approximate a locally unique solution of a nonlinear equation in a Banach space setting. The Frechet-derivative of the operator involved is not necessarily continuous invertible. This way we extend the applicability of Newton-typ...

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Autores principales:	Argyros,Ioannis K, Hilout,Saïd
Lenguaje:	English
Publicado:	Universidad de La Frontera. Departamento de Matemática y Estadística. 2011
Materias:	Newton-type methods Banach space small divisors non-invertible operators semilocal convergence Newton-Kantorovich-type hypothesis.
Acceso en línea:	http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0719-06462011000300001
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spelling	oai:scielo:S0719-064620110003000012018-10-08On the semilocal convergence of Newton-type methods, when the derivative is not continuously invertibleArgyros,Ioannis KHilout,Saïd Newton-type methods Banach space small divisors non-invertible operators semilocal convergence Newton-Kantorovich-type hypothesis. We provide a semilocal convergence analysis for Newton-type methods to approximate a locally unique solution of a nonlinear equation in a Banach space setting. The Frechet-derivative of the operator involved is not necessarily continuous invertible. This way we extend the applicability of Newton-type methods &#0911]-[12]. We also provide weaker sufficient convergence conditions, and finer error bound on the distances involved (under the same computational cost) than [1]-[12], in some intersting cases. Numerical examples are also provided in this study.info:eu-repo/semantics/openAccessUniversidad de La Frontera. Departamento de Matemática y Estadística.Cubo (Temuco) v.13 n.3 20112011-10-01text/htmlhttp://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0719-06462011000300001en10.4067/S0719-06462011000300001
institution	Scielo Chile
collection	Scielo Chile
language	English
topic	Newton-type methods Banach space small divisors non-invertible operators semilocal convergence Newton-Kantorovich-type hypothesis.
spellingShingle	Newton-type methods Banach space small divisors non-invertible operators semilocal convergence Newton-Kantorovich-type hypothesis. Argyros,Ioannis K Hilout,Saïd On the semilocal convergence of Newton-type methods, when the derivative is not continuously invertible
description	We provide a semilocal convergence analysis for Newton-type methods to approximate a locally unique solution of a nonlinear equation in a Banach space setting. The Frechet-derivative of the operator involved is not necessarily continuous invertible. This way we extend the applicability of Newton-type methods &#0911]-[12]. We also provide weaker sufficient convergence conditions, and finer error bound on the distances involved (under the same computational cost) than [1]-[12], in some intersting cases. Numerical examples are also provided in this study.
author	Argyros,Ioannis K Hilout,Saïd
author_facet	Argyros,Ioannis K Hilout,Saïd
author_sort	Argyros,Ioannis K
title	On the semilocal convergence of Newton-type methods, when the derivative is not continuously invertible
title_short	On the semilocal convergence of Newton-type methods, when the derivative is not continuously invertible
title_full	On the semilocal convergence of Newton-type methods, when the derivative is not continuously invertible
title_fullStr	On the semilocal convergence of Newton-type methods, when the derivative is not continuously invertible
title_full_unstemmed	On the semilocal convergence of Newton-type methods, when the derivative is not continuously invertible
title_sort	on the semilocal convergence of newton-type methods, when the derivative is not continuously invertible
publisher	Universidad de La Frontera. Departamento de Matemática y Estadística.
publishDate	2011
url	http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0719-06462011000300001
work_keys_str_mv	AT argyrosioannisk onthesemilocalconvergenceofnewtontypemethodswhenthederivativeisnotcontinuouslyinvertible AT hiloutsaid onthesemilocalconvergenceofnewtontypemethodswhenthederivativeisnotcontinuouslyinvertible
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On the semilocal convergence of Newton-type methods, when the derivative is not continuously invertible

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