A study of dynamics via Mobius conjugacy map on a family of sixth-order modified Newton-like multiple-zero finders with bivariate polynomial weight functions - Geum, Young Hee; Kim, Young Ik; Magreñán, Á. Alberto (Journal of Computational and Applied Mathematics, 2019)
A generic family of sixth-order modified Newton-like multiple-zero finders have been proposed in Geum et al. (2016). Among them we select a specific family of iterative methods with uniparametric bivariate polynomial weight functions and study their dynamics by investigating the relevant parameter spaces and dynamical planes, via Mobius conjugacy map applied to a prototype polynomial of the form (z-a)(m) (z-b)(m). The resulting dynamics is best illustrated through a variety of parameter spaces as well as dynamical planes.
Keywords: parameter space; mobius map; dynamical plane; multiple-zero; sixth-order; conjugacy; JCR; Scopus