A highly efficient root-solver of very fast convergence

The improved iterative method of Ehrlich–Aberth’s type for the simultaneous determination of all simple complex zeros of a polynomial is proposed. The presented convergence analysis shows that the convergence rate of the basic third order method is increased from 3 to 6 using Ostrowski’s corrections. The new iterative method is more efficient compared to all existing methods based on fixed point relations. Some computational aspects and numerical examples are given.