Sergio AmatHonorato, GerardoGerardoHonoratoÁ. A. MagreñánCastro, RodrigoRodrigoCastro2025-04-132025-04-132020-07-1510.3390/math80711582-s2.0-85088667463https://cris-uv-2.scimago.es/handle/123456789/2059WOS:000557042100001The 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.enacceso abiertoMathematicsarticle