Abstract
In this paper, we first recall the definition of a family of root-finding algorithms known as König's algorithms. We establish some local and some global properties of those algorithms. We give a characterization of rational maps which arise as König's methods of polynomials with simple roots. We then estimate the number of non-repelling cycles König's methods of polynomials may have. We finally study the geometry of the Julia sets of König's methods of polynomials and produce pictures of parameter spaces for König's methods of cubic polynomials.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
