Semilocal convergence of Chebyshev-like root-finding method for simultaneous approximation of polynomial zeros

Abstract

In this paper, we present convergence results for the Chebyshev-like method for the simultaneous computation of all zeros of a polynomial f over a complete normed field. Our results generalize, improve and complement the result of Petković and Petković (2001) [10]. The new results give weaker sufficient convergence conditions, a priori and a posteriori error estimates as well as information on the location of the zeros. Another important aspect of this work is that we do not assume neither simplicity nor existence of the zeros of f. Furthermore, several numerical examples are provided to show some practical applications of our results.