A unified semilocal convergence analysis of a family of iterative algorithms for computing all zeros of a polynomial simultaneously

In this paper, we first present a family of iterative algorithms for simultaneous determination of all zeros of a polynomial. This family contains two well-known algorithms: Dochev-Byrnev’s method and Ehrlich’s method. Second, using Proinov’s approach to studying convergence of iterative methods for polynomial zeros, we provide a semilocal convergence theorem that unifies the results of Proinov (Appl. Math. Comput. 284: 102–114, 2016) for Dochev-Byrnev’s and Ehrlich’s methods.