Extended domain for fifth convergence order schemes

Abstract We provide a local as well as a semi-local analysis of a fifth convergence order scheme involving operators valued on Banach space for solving nonlinear equations. The convergence domain is extended resulting a finer convergence analysis for both types. This is achieved by locating a smalle...

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Autores principales:	Argyros,Ioannis K., George,Santhosh
Lenguaje:	English
Publicado:	Universidad de La Frontera. Departamento de Matemática y Estadística. 2021
Materias:	Fifth order convergence scheme w-continuity convergence analysis Fréchet derivative Banach space.
Acceso en línea:	http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0719-06462021000100097
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spelling	oai:scielo:S0719-064620210001000972021-05-11Extended domain for fifth convergence order schemesArgyros,Ioannis K.George,Santhosh Fifth order convergence scheme w-continuity convergence analysis Fréchet derivative Banach space. Abstract We provide a local as well as a semi-local analysis of a fifth convergence order scheme involving operators valued on Banach space for solving nonlinear equations. The convergence domain is extended resulting a finer convergence analysis for both types. This is achieved by locating a smaller domain included in the older domain leading this way to tighter Lipschitz type functions. These extensions are obtained without additional hypotheses. Numerical examples are used to test the convergence criteria and also to show the superiority for our results over earlier ones. Our idea can be utilized to extend other schemes using inverses in a similar way.info:eu-repo/semantics/openAccessUniversidad de La Frontera. Departamento de Matemática y Estadística.Cubo (Temuco) v.23 n.1 20212021-01-01text/htmlhttp://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0719-06462021000100097en10.4067/S0719-06462021000100097
institution	Scielo Chile
collection	Scielo Chile
language	English
topic	Fifth order convergence scheme w-continuity convergence analysis Fréchet derivative Banach space.
spellingShingle	Fifth order convergence scheme w-continuity convergence analysis Fréchet derivative Banach space. Argyros,Ioannis K. George,Santhosh Extended domain for fifth convergence order schemes
description	Abstract We provide a local as well as a semi-local analysis of a fifth convergence order scheme involving operators valued on Banach space for solving nonlinear equations. The convergence domain is extended resulting a finer convergence analysis for both types. This is achieved by locating a smaller domain included in the older domain leading this way to tighter Lipschitz type functions. These extensions are obtained without additional hypotheses. Numerical examples are used to test the convergence criteria and also to show the superiority for our results over earlier ones. Our idea can be utilized to extend other schemes using inverses in a similar way.
author	Argyros,Ioannis K. George,Santhosh
author_facet	Argyros,Ioannis K. George,Santhosh
author_sort	Argyros,Ioannis K.
title	Extended domain for fifth convergence order schemes
title_short	Extended domain for fifth convergence order schemes
title_full	Extended domain for fifth convergence order schemes
title_fullStr	Extended domain for fifth convergence order schemes
title_full_unstemmed	Extended domain for fifth convergence order schemes
title_sort	extended domain for fifth convergence order schemes
publisher	Universidad de La Frontera. Departamento de Matemática y Estadística.
publishDate	2021
url	http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0719-06462021000100097
work_keys_str_mv	AT argyrosioannisk extendeddomainforfifthconvergenceorderschemes AT georgesanthosh extendeddomainforfifthconvergenceorderschemes
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Extended domain for fifth convergence order schemes

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