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, issue 1

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 m. A 600 × 600 uniform grid centered at the origin covering 6 × 6 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
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https://doi.org/10.1155/2016/8436759

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnddns:v:2016:y:2016:i:1:n:8436759

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