Finding all Zeros of a Polynomial by Simultaneous Methods

The purpose of this paper is to present new method for finding all simple zeros of polynomials simultaneously. First, we give a new method for finding simultaneously all simple zeros of polynomials constructed by applying the Weierstrass method to the zero in the trapezoidal Newton’s method, and prove the convergence of the method. Finally, we give a numerical comparison between various simultaneous methods for finding zeros of a polynomial.