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
Description
Summary: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.
ISSN:1989-1660
1989-1660

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