The self-validated method for polynomial zeros of high efficiency

The improved iterative method of Newton’s type for the simultaneous inclusion of all simple complex zeros of a polynomial is proposed. The presented convergence analysis, which uses the concept of the R-order of convergence of mutually dependent sequences, shows that the convergence rate of the basic third order method is increased from 3 to 6 using Ostrowski’s corrections. The new inclusion method with Ostrowski’s corrections is more efficient compared to all existing methods belonging to the same class. To demonstrate the convergence properties of the proposed method, two numerical examples are given.