In this paper, we revisit the convergence properties of the iteration process x(k+1) = x(k) – α(x(k))B(x(k))–1Δf(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. Not only this result gives a new algorithmic interpretation to the classic Ostrowski theorem, but also provides insight into the interesting phenomenon called selective minimization. We present also illustrative numerical examples for nonlinear least squares problems.
