  In this paper, we establish a general semilocal convergence theorem (with
computationally verifiable initial conditions and error estimates) for
iterative methods for simultaneous approximation of polynomial zeros. As
application of this theorem, we provide new semilocal convergence results for
Ehrlich's and Dochev-Byrnev's root-finding methods. These results improve the
results of Petkovi\'c, Herceg and Ili\'c [Numer. Algorithms 17 (1998) 313--331]
and Proinov [C.~R. Acad. Bulg. Sci. 59 (2006) 705--712]. We also prove that
Dochev-Byrnev's method (1964) is identical to Pre{\v s}i\'c-Tanabe's method
(1972).
