On the convergence order of a modified method for simultaneous finding polynomial zeros

Abstract

Using Newton's corrections and Gauss-Seidel approach, a modification of single-step method [1] for the simultaneous finding all zeros of ann-th degree polynomial is formulated in this paper. It is shown thatR-order of convergence of the presented method is at least 2(1+τ n ) where τ n ∈(1,2) is the unique positive zero of the polynomial $$\tilde f_n (\tau ) = \tau ^n - \tau - 1$$ . Faster convergence of the modified method in reference to the similar methods is attained without additional calculations. Comparison is performed in the example of an algebraic equation.