CONVERGENCE OF NEWTON'S METHOD UNDER THE GAMMA CONDITION

CONVERGENCE OF NEWTON'S METHOD UNDER THE GAMMA CONDITION

We provide a semilocal as well as a local convergence analysis ofNewton's method using the gamma condition [1], [10], [11]. Usingmore precise majorizing sequences than before [4], [8]-[11] and underat least as weak hypotheses, we provide in the semilocal case: finererror bounds on the distances...

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Autor principal: ARGYROS,IOANNIS K
Lenguaje:English
Publicado: Universidad Católica del Norte, Departamento de Matemáticas 2006
Materias:
Banach space
Newton's method
local/semilocalconvergence
Newton-Kantorovich theorem
Fréchet derivative
majorizingsequence
radius of convergence
gamma condition
analyticoperator
Acceso en línea:http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172006000300006
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spelling oai:scielo:S0716-091720060003000062007-03-21CONVERGENCE OF NEWTON'S METHOD UNDER THE GAMMA CONDITIONARGYROS,IOANNIS K Banach space Newton's method local/semilocalconvergence Newton-Kantorovich theorem Fréchet derivative majorizingsequence radius of convergence gamma condition analyticoperator We provide a semilocal as well as a local convergence analysis ofNewton's method using the gamma condition [1], [10], [11]. Usingmore precise majorizing sequences than before [4], [8]-[11] and underat least as weak hypotheses, we provide in the semilocal case: finererror bounds on the distances involved and an at least as precise informationon the location of the solution; in the local case: a largerradius of convergenceinfo:eu-repo/semantics/openAccessUniversidad Católica del Norte, Departamento de MatemáticasProyecciones (Antofagasta) v.25 n.3 20062006-12-01text/htmlhttp://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172006000300006en10.4067/S0716-09172006000300006
institution Scielo Chile
collection Scielo Chile
language English
topic Banach space
Newton's method
local/semilocalconvergence
Newton-Kantorovich theorem
Fréchet derivative
majorizingsequence
radius of convergence
gamma condition
analyticoperator
spellingShingle Banach space
Newton's method
local/semilocalconvergence
Newton-Kantorovich theorem
Fréchet derivative
majorizingsequence
radius of convergence
gamma condition
analyticoperator
ARGYROS,IOANNIS K
CONVERGENCE OF NEWTON'S METHOD UNDER THE GAMMA CONDITION
description We provide a semilocal as well as a local convergence analysis ofNewton's method using the gamma condition [1], [10], [11]. Usingmore precise majorizing sequences than before [4], [8]-[11] and underat least as weak hypotheses, we provide in the semilocal case: finererror bounds on the distances involved and an at least as precise informationon the location of the solution; in the local case: a largerradius of convergence
author ARGYROS,IOANNIS K
author_facet ARGYROS,IOANNIS K
author_sort ARGYROS,IOANNIS K
title CONVERGENCE OF NEWTON'S METHOD UNDER THE GAMMA CONDITION
title_short CONVERGENCE OF NEWTON'S METHOD UNDER THE GAMMA CONDITION
title_full CONVERGENCE OF NEWTON'S METHOD UNDER THE GAMMA CONDITION
title_fullStr CONVERGENCE OF NEWTON'S METHOD UNDER THE GAMMA CONDITION
title_full_unstemmed CONVERGENCE OF NEWTON'S METHOD UNDER THE GAMMA CONDITION
title_sort convergence of newton's method under the gamma condition
publisher Universidad Católica del Norte, Departamento de Matemáticas
publishDate 2006
url http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172006000300006
work_keys_str_mv AT argyrosioannisk convergenceofnewtonsmethodunderthegammacondition
_version_ 1718439749550604288

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