Study of iterative methods through the Cayley Quadratic Test

Many iterative methods for solving nonlinear equations have been developed recently. The main advantage claimed by their authors is the improvement of the order of convergence. In this work, we compare their dynamical behavior on quadratic polynomials with the one of Newton’s scheme. This comparison is defined in what we call Cayley Quadratic Test (CQT) which can be used as a first test to check the efficiency of such methods. Moreover we make a brief insight in cubic polynomials.