Point estimation of a family of simultaneous zero-finding methods

The construction of initial conditions which provide the safe convergence of iterative processes is one of the most important problems in solving equations. In this paper, we give initial conditions for a one parameter family of iterative methods for the simultaneous determination of all simple zeros of a polynomial zeros. This family has the order of convergence four and generates some new methods with good convergence properties. The presented initial conditions are of practical importance since depend only of available data: coefficients of a polynomial and initial approximations to the zeros.