  The construction of initial conditions of an iterative method is one of the
most important problems in solving nonlinear equations. In this paper, we
obtain relationships between different types of initial conditions that
guarantee the convergence of iterative methods for simultaneous finding all
zeros of a polynomial. In particular, we show that any local convergence
theorem for a simultaneous method can be converted into a convergence theorem
with computationally verifiable initial conditions which is of practical
importance. Thus, we propose a new approach for obtaining semilocal convergence
results for simultaneous methods via local convergence results.

Numerical Analysis;Classical Analysis and ODEs