Lower bounds for the \(R\)-order of convergence of simultaneous inclusion methods for polynomial roots and related iteration methods (Q1900748)

There exists a huge number of iterative algorithms for approximating the roots of a given polynomial. The authors are discussing very general families of simultaneous inclusion methods, that is to say algorithms determining the roots of a given polynomial with respect to a given set. In order to compare these methods one can look at the so-called \(R\)- order, which describes the local speed of convergence and thereby provides an efficiency measure. The main result is an explicit lower bound for the \(R\)-order depending on the parameters of the given method.