ON THE LOCAL CONVERGENCE OF A TWO-STEP STEFFENSEN-TYPE METHOD FOR SOLVING GENERALIZED EQUATIONS

ON THE LOCAL CONVERGENCE OF A TWO-STEP STEFFENSEN-TYPE METHOD FOR SOLVING GENERALIZED EQUATIONS

We use a two-step Steffensen-type method [1], [2], [4], [6], [13]-[16] to solve a generalized equation in a Banach space setting under Hölder-type conditions introduced by us in [2], [6] for nonlinear equations. Using some ideas given in [4], [6] for nonlinear equations, we provide a local convergen...

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Autores principales: ARGYROS,IOANNIS K, HILOUT,SAÏD
Lenguaje:English
Publicado: Universidad Católica del Norte, Departamento de Matemáticas 2008
Materias:
Banach space
Steffensen’s method
generalized equation
Aubin continuity
Hölder continuity
radius of convergence
divided difference
set- valued map
Acceso en línea:http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172008000300007
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spelling oai:scielo:S0716-091720080003000072009-01-13ON THE LOCAL CONVERGENCE OF A TWO-STEP STEFFENSEN-TYPE METHOD FOR SOLVING GENERALIZED EQUATIONSARGYROS,IOANNIS KHILOUT,SAÏD Banach space Steffensen’s method generalized equation Aubin continuity Hölder continuity radius of convergence divided difference set- valued map We use a two-step Steffensen-type method [1], [2], [4], [6], [13]-[16] to solve a generalized equation in a Banach space setting under Hölder-type conditions introduced by us in [2], [6] for nonlinear equations. Using some ideas given in [4], [6] for nonlinear equations, we provide a local convergence analysis with the following advantages over related [13]-[16]: finer error bounds on the distances involved, and a larger radius of convergence. An application is also provided.info:eu-repo/semantics/openAccessUniversidad Católica del Norte, Departamento de MatemáticasProyecciones (Antofagasta) v.27 n.3 20082008-12-01text/htmlhttp://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172008000300007en10.4067/S0716-09172008000300007
institution Scielo Chile
collection Scielo Chile
language English
topic Banach space
Steffensen’s method
generalized equation
Aubin continuity
Hölder continuity
radius of convergence
divided difference
set- valued map
spellingShingle Banach space
Steffensen’s method
generalized equation
Aubin continuity
Hölder continuity
radius of convergence
divided difference
set- valued map
ARGYROS,IOANNIS K
HILOUT,SAÏD
ON THE LOCAL CONVERGENCE OF A TWO-STEP STEFFENSEN-TYPE METHOD FOR SOLVING GENERALIZED EQUATIONS
description We use a two-step Steffensen-type method [1], [2], [4], [6], [13]-[16] to solve a generalized equation in a Banach space setting under Hölder-type conditions introduced by us in [2], [6] for nonlinear equations. Using some ideas given in [4], [6] for nonlinear equations, we provide a local convergence analysis with the following advantages over related [13]-[16]: finer error bounds on the distances involved, and a larger radius of convergence. An application is also provided.
author ARGYROS,IOANNIS K
HILOUT,SAÏD
author_facet ARGYROS,IOANNIS K
HILOUT,SAÏD
author_sort ARGYROS,IOANNIS K
title ON THE LOCAL CONVERGENCE OF A TWO-STEP STEFFENSEN-TYPE METHOD FOR SOLVING GENERALIZED EQUATIONS
title_short ON THE LOCAL CONVERGENCE OF A TWO-STEP STEFFENSEN-TYPE METHOD FOR SOLVING GENERALIZED EQUATIONS
title_full ON THE LOCAL CONVERGENCE OF A TWO-STEP STEFFENSEN-TYPE METHOD FOR SOLVING GENERALIZED EQUATIONS
title_fullStr ON THE LOCAL CONVERGENCE OF A TWO-STEP STEFFENSEN-TYPE METHOD FOR SOLVING GENERALIZED EQUATIONS
title_full_unstemmed ON THE LOCAL CONVERGENCE OF A TWO-STEP STEFFENSEN-TYPE METHOD FOR SOLVING GENERALIZED EQUATIONS
title_sort on the local convergence of a two-step steffensen-type method for solving generalized equations
publisher Universidad Católica del Norte, Departamento de Matemáticas
publishDate 2008
url http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172008000300007
work_keys_str_mv AT argyrosioannisk onthelocalconvergenceofatwostepsteffensentypemethodforsolvinggeneralizedequations
AT hiloutsaid onthelocalconvergenceofatwostepsteffensentypemethodforsolvinggeneralizedequations
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