A Triparametric Family of Optimal Fourth-Order Multiple-Root Finders and Their Dynamics

Young Ik Kim and Young Hee Geum

Discrete Dynamics in Nature and Society, 2016, vol. 2016, 1-23

Abstract:

We investigate the complex dynamics of a triparametric family of optimal fourth-order multiple-root solvers by analyzing their basins of attraction along with extensive study of Möbius conjugacy maps and extraneous fixed points applied to a prototype quadratic polynomial raised to the power of the known integer multiplicity . A uniform grid centered at the origin covering square region is chosen to display the initial points on each basin of attraction according to a coloring scheme based on their orbit behavior. With illustrative basins of attractions applied to various test polynomials and the corresponding statistical data for convergence as well as a number of comparisons made among the listed methods, we confirm our investigation and analysis developed in this paper.

Date: 2016
References: Add references at CitEc
Citations:

Downloads: (external link)
http://downloads.hindawi.com/journals/DDNS/2016/8436759.pdf (application/pdf)
http://downloads.hindawi.com/journals/DDNS/2016/8436759.xml (text/xml)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:hin:jnddns:8436759

DOI: 10.1155/2016/8436759

Access Statistics for this article

More articles in Discrete Dynamics in Nature and Society from Hindawi
Bibliographic data for series maintained by Mohamed Abdelhakeem ().