Extending the Applicability of the Super-Halley-Like Method Using ω-Continuous Derivatives and Restricted Convergence Domains

Extending the Applicability of the Super-Halley-Like Method Using ω-Continuous Derivatives and Restricted Convergence Domains

We present a local convergence analysis of the super-Halley-like method in order to approximate a locally unique solution of an equation in a Banach space setting. The convergence analysis in earlier studies was based on hypotheses reaching up to the third derivative of the operator. In the present...

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Main Authors: Argyros Ioannis K., George Santhosh
Format: Article
Language:English
Published: Sciendo 2019-09-01
Series:Annales Mathematicae Silesianae
Subjects:
super-Halley-like method
Banach space
local convergence
Fréchet derivative
65D10
65D99
Online Access:http://www.degruyter.com/view/j/amsil.2019.33.issue-1/amsil-2018-0008/amsil-2018-0008.xml?format=INT
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spelling doaj-ff71e582be7e46d8a654db4506434c9f2020-11-24T22:26:11ZengSciendoAnnales Mathematicae Silesianae2391-42382019-09-01331214010.2478/amsil-2018-0008amsil-2018-0008Extending the Applicability of the Super-Halley-Like Method Using ω-Continuous Derivatives and Restricted Convergence DomainsArgyros Ioannis K.0George Santhosh1Department of Mathematical Sciences, Cameron University, Lawton, OK 73505, USADepartment of Mathematical and Computational Sciences, National Institute of Technology Karnataka, 575 025 Karnataka, IndiaWe present a local convergence analysis of the super-Halley-like method in order to approximate a locally unique solution of an equation in a Banach space setting. The convergence analysis in earlier studies was based on hypotheses reaching up to the third derivative of the operator. In the present study we expand the applicability of the super-Halley-like method by using hypotheses up to the second derivative. We also provide: a computable error on the distances involved and a uniqueness result based on Lipschitz constants. Numerical examples are also presented in this study.http://www.degruyter.com/view/j/amsil.2019.33.issue-1/amsil-2018-0008/amsil-2018-0008.xml?format=INTsuper-Halley-like methodBanach spacelocal convergenceFréchet derivative65D1065D99
collection DOAJ
language English
format Article
sources DOAJ
author Argyros Ioannis K.
George Santhosh
spellingShingle Argyros Ioannis K.
George Santhosh
Extending the Applicability of the Super-Halley-Like Method Using ω-Continuous Derivatives and Restricted Convergence Domains
Annales Mathematicae Silesianae
super-Halley-like method
Banach space
local convergence
Fréchet derivative
65D10
65D99
author_facet Argyros Ioannis K.
George Santhosh
author_sort Argyros Ioannis K.
title Extending the Applicability of the Super-Halley-Like Method Using ω-Continuous Derivatives and Restricted Convergence Domains
title_short Extending the Applicability of the Super-Halley-Like Method Using ω-Continuous Derivatives and Restricted Convergence Domains
title_full Extending the Applicability of the Super-Halley-Like Method Using ω-Continuous Derivatives and Restricted Convergence Domains
title_fullStr Extending the Applicability of the Super-Halley-Like Method Using ω-Continuous Derivatives and Restricted Convergence Domains
title_full_unstemmed Extending the Applicability of the Super-Halley-Like Method Using ω-Continuous Derivatives and Restricted Convergence Domains
title_sort extending the applicability of the super-halley-like method using ω-continuous derivatives and restricted convergence domains
publisher Sciendo
series Annales Mathematicae Silesianae
issn 2391-4238
publishDate 2019-09-01
description We present a local convergence analysis of the super-Halley-like method in order to approximate a locally unique solution of an equation in a Banach space setting. The convergence analysis in earlier studies was based on hypotheses reaching up to the third derivative of the operator. In the present study we expand the applicability of the super-Halley-like method by using hypotheses up to the second derivative. We also provide: a computable error on the distances involved and a uniqueness result based on Lipschitz constants. Numerical examples are also presented in this study.
topic super-Halley-like method
Banach space
local convergence
Fréchet derivative
65D10
65D99
url http://www.degruyter.com/view/j/amsil.2019.33.issue-1/amsil-2018-0008/amsil-2018-0008.xml?format=INT
work_keys_str_mv AT argyrosioannisk extendingtheapplicabilityofthesuperhalleylikemethodusingōcontinuousderivativesandrestrictedconvergencedomains
AT georgesanthosh extendingtheapplicabilityofthesuperhalleylikemethodusingōcontinuousderivativesandrestrictedconvergencedomains
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