Dynamics of Newton-like root finding methods

Abstract When exploring the literature, it can be observed that operator obtained when applying Newton-like root finding algorithms to quadratic polynomials z 2 − c has same form regardless of which algorithm been used. In this paper, we justify why expression is obtained. This done by studying symmetries operators after a family degree d p ( ) = . Moreover, provide an iterative procedure obtain new algorithms. We also carry out dynamical study given generic and general conclusions type methods.