Basins of Attraction for Various Steffensen-Type Methods release_iyaqqnzwv5f4ljaeqoj4rust4a

by Alicia Cordero, Fazlollah Soleymani, Juan R. Torregrosa, Stanford Shateyi

Published in Journal of Applied Mathematics by Hindawi Limited.

2014   Volume 2014, p1-17

Abstract

The dynamical behavior of different Steffensen-type methods is analyzed. We check the chaotic behaviors alongside the convergence radii (understood as the wideness of the basin of attraction) needed by Steffensen-type methods, that is, derivative-free iteration functions, to converge to a root and compare the results using different numerical tests. We will conclude that the convergence radii (and the stability) of Steffensen-type methods are improved by increasing the convergence order. The computer programming package M<jats:sc>ATHEMATICA</jats:sc>provides a powerful but easy environment for all aspects of numerics. This paper puts on show one of the application of this computer algebra system in finding fixed points of iteration functions.
In application/xml+jats format

Archived Files and Locations

application/pdf  9.9 MB
file_6crxeqq4kjf3vpf2csq4ruo7om
downloads.hindawi.com (publisher)
web.archive.org (webarchive)
application/pdf  8.1 MB
file_bseim4dxxbbgblr2dbst4dxh7a
riunet.upv.es (web)
web.archive.org (webarchive)
application/pdf  8.5 MB
file_pqzoh3wjgvdtxdoqukv5ujrpgq
projecteuclid.org (web)
web.archive.org (webarchive)
Read Archived PDF
Preserved and Accessible
Type  article-journal
Stage   published
Year   2014
Language   en ?
Journal Metadata
Open Access Publication
In DOAJ
In ISSN ROAD
In Keepers Registry
ISSN-L:  1110-757X
Work Entity
access all versions, variants, and formats of this works (eg, pre-prints)
Catalog Record
Revision: 5a76b2c7-b91c-48c5-8a59-aec72985a673
API URL: JSON