In this paper, we revisit the convergence properties of the iteration process x k+1 = x k \Gamma ff(x k )B(x k ) \Gamma1 rf(x k ) for minimizing a function f(x). After reviewing some classic results and introducing the notion of strong attraction, we give necessary and sufficient conditions for a stationary point of f(x) to be a point of strong attraction for the iteration process. This result not only gives a new algorithmic interpretation to the classic Ostrowski theorem, but also provides insight into the interesting phenomenon called selective minimization. We also present illustrative numerical examples for nonlinear least squares problems. Keywords: Attraction, repulsion, selective minimization 1.