Convergence analysis of Sakurai–Torii–Sugiura iterative method for simultaneous approximation of polynomial zeros.

Abstract In 1991, T. Sakurai, T. Torii and H. Sugiura presented a fourth-order iterative algorithm for finding all zeros of a polynomial simultaneously. In this paper, we provide a detailed convergence analysis (local and semilocal) of this method. The new results improve and complement existing results due to Petković et al. (2003) and Petković (2008). Numerical examples are given to show the applicability of our semilocal convergence results. [ABSTRACT FROM AUTHOR]