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

• Main Authors: Young Ik Kim, Young Hee Geum
• Format: Article
• Language: English
• Published: Hindawi Limited 2016-01-01
• Series: Discrete Dynamics in Nature and Society
• Online Access: http://dx.doi.org/10.1155/2016/8436759

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.