On a simultaneous method of Newton-Weierstrass' type for finding all zeros of a polynomial

Combining a suitable two-point iterative method for solving nonlinear equations and Weierstrass' correction, a new iterative method for simultaneous finding all zeros of a polynomial is derived. It is proved that the proposed method possesses a cubic convergence locally. Numerical examples demonstrate a good convergence behavior of this method in a global sense. It is shown that its computational efficiency is higher than the existing derivative-free methods.