Local Convergence for an Improved Jarratt-type Method in Banach Space

Local Convergence for an Improved Jarratt-type Method in Banach Space

We present a local convergence analysis for an improved Jarratt-type methods of order at least five to approximate a solution of a nonlinear equation in a Banach space setting. The convergence ball and error estimates are given using hypotheses up to the first Fréchet derivative in contrast to earl...

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Bibliographic Details
Main Authors: Ioannis Argyros, Daniel González
Format: Article
Language:English
Published: Universidad Internacional de La Rioja (UNIR) 2015-08-01
Series:International Journal of Interactive Multimedia and Artificial Intelligence
Subjects:
Banach Space
Jarratt-type Methods
Local Convergence
Newton’s Method
Online Access:http://www.ijimai.org/journal/node/802
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spelling doaj-4a6b5478c53442138ad9f5dae94c25562020-11-24T21:22:58ZengUniversidad Internacional de La Rioja (UNIR)International Journal of Interactive Multimedia and Artificial Intelligence1989-16601989-16602015-08-0134202510.9781/ijimai.2015.345ijimai.2015.345Local Convergence for an Improved Jarratt-type Method in Banach SpaceIoannis ArgyrosDaniel GonzálezWe present a local convergence analysis for an improved Jarratt-type methods of order at least five to approximate a solution of a nonlinear equation in a Banach space setting. The convergence ball and error estimates are given using hypotheses up to the first Fréchet derivative in contrast to earlier studies using hypotheses up to the third Fréchet derivative. Numerical examples are also provided in this study, where the older hypotheses are not satisfied to solve equations but the new hypotheses are satisfied.http://www.ijimai.org/journal/node/802Banach SpaceJarratt-type MethodsLocal ConvergenceNewton’s Method
collection DOAJ
language English
format Article
sources DOAJ
author Ioannis Argyros
Daniel González
spellingShingle Ioannis Argyros
Daniel González
Local Convergence for an Improved Jarratt-type Method in Banach Space
International Journal of Interactive Multimedia and Artificial Intelligence
Banach Space
Jarratt-type Methods
Local Convergence
Newton’s Method
author_facet Ioannis Argyros
Daniel González
author_sort Ioannis Argyros
title Local Convergence for an Improved Jarratt-type Method in Banach Space
title_short Local Convergence for an Improved Jarratt-type Method in Banach Space
title_full Local Convergence for an Improved Jarratt-type Method in Banach Space
title_fullStr Local Convergence for an Improved Jarratt-type Method in Banach Space
title_full_unstemmed Local Convergence for an Improved Jarratt-type Method in Banach Space
title_sort local convergence for an improved jarratt-type method in banach space
publisher Universidad Internacional de La Rioja (UNIR)
series International Journal of Interactive Multimedia and Artificial Intelligence
issn 1989-1660
1989-1660
publishDate 2015-08-01
description We present a local convergence analysis for an improved Jarratt-type methods of order at least five to approximate a solution of a nonlinear equation in a Banach space setting. The convergence ball and error estimates are given using hypotheses up to the first Fréchet derivative in contrast to earlier studies using hypotheses up to the third Fréchet derivative. Numerical examples are also provided in this study, where the older hypotheses are not satisfied to solve equations but the new hypotheses are satisfied.
topic Banach Space
Jarratt-type Methods
Local Convergence
Newton’s Method
url http://www.ijimai.org/journal/node/802
work_keys_str_mv AT ioannisargyros localconvergenceforanimprovedjarratttypemethodinbanachspace
AT danielgonzalez localconvergenceforanimprovedjarratttypemethodinbanachspace
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