Purely Iterative Algorithms for Newton’s Maps and General Convergence - Amat, Sergio; Castro, Rodrigo; Honorato, Gerardo; Magreñán, Á. A. (Mathematics (Basel), 2020)
The aim of this paper is to study the local dynamical behaviour of a broad class of purely iterative algorithms for Newton’s maps. In particular, we describe the nature and stability of fixed points and provide a type of scaling theorem. Based on those results, we apply a rigidity theorem in order to study the parameter space of cubic polynomials, for a large class of new root finding algorithms. Finally, we study the relations between critical points and the parameter space.