Smale's condition for a point to be an approximate zero of a function for Newton's method is extended to the general quadratically convergent iterative algorithm. It is shown in which way the bound in the condition is affected by the characteristics of the algorithm. This puts the original condition of Smale for Newton's method in a more general perspective. The results are also discussed in the light of numerical evidence. |z/k+i-z*|< I 2 1 l2i-zo|, k = 0, 1,2, ... . Under this definition, Smale [8] proved the following theorem that gives a