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

TitleLocal Convergence for an Improved Jarratt-type Method in Banach Space
Publication TypeJournal Article
Year of Publication2015
AuthorsArgyros, I. K., and D. González
JournalInternational Journal of Interactive Multimedia and Artificial Intelligence
ISSN1989-1660
IssueSpecial Issue on Teaching Mathematics Using New and Classic Tools
Volume3
Number4
Date Published09/2015
Pagination20-25
Abstract

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.

KeywordsBanach Space, Jarratt-type Methods, Local Convergence, Newton’s Method
DOI10.9781/ijimai.2015.344
URLhttp://www.ijimai.org/JOURNAL/sites/default/files/files/2015/08/ijimai20153_4_4_pdf_25787.pdf
AttachmentSize
ijimai20153_4_4.pdf1.18 MB