A Graphic Method for Detecting Multiple Roots Based on Self-Maps of the Hopf Fibration and Nullity Tolerances

The aim of this paper is to study, from a topological and geometrical point view, the iteration map obtained by application iterative methods (Newton or relaxed Newton’s method) polynomial equation. In fact, we present collection algorithms that avoid problem overflows caused denominators close zero indetermination which appears when simultaneously numerator denominator are equal zero. This solved working with homogeneous coordinates self-maps Hopf fibration. As an application, our can be used check existence multiple roots for equations as well give graphical representation union basins attraction simple roots. Finally, would like highlight all developed in work have been implemented Julia, programming language increasing use mathematical community.