Ball Convergence for Steffensen-type Fourth-order Methods

TitleBall Convergence for Steffensen-type Fourth-order Methods
Publication TypeJournal Article
Year of Publication2015
AuthorsArgyros, I. K., and S. George
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
Pagination37-42
Abstract

We present a local convergence analysis for a family of Steffensen-type fourth-order methods in order to approximate a solution of a nonlinear equation. We use hypotheses up to the first derivative in contrast to earlier studies such as [1], [5]-[28] using hypotheses up to the fifth derivative. This way the applicability of these methods is extended under weaker hypotheses. Moreover the radius of convergence and computable error bounds on the distances involved are also given in this study. Numerical examples are also presented in this study.

KeywordsLocal Convergence, Newton’s Method, Steffensen-type Method
DOI10.9781/ijimai.2015.347
URLhttp://www.ijimai.org/JOURNAL/sites/default/files/files/2015/08/ijimai20153_4_7_pdf_73265.pdf
AttachmentSize
ijimai20153_4_7.pdf3.53 MB