Lower bounds for the R-order of convergence of simultaneous inclusion methods for polynomial roots and related iteration methods

The purpose of this paper is to give a survey on recent results concerning the estimation of the R-order of convergence of some classes of single-step iteration methods. We are dealing with some very general families of simultaneous inclusion methods for polynomial zeros and with error-recursions generalized by those of these families. It is shown how in these cases explicit lower bounds can be derived for the R-order depending on the parameters of the methods.