On the accelerating property of an algorithm for function minimization without calculating derivatives

It is shown that the alogrithm of Ref. E1, when converging on a uniformly convex function and when technical condition (13) of Ref. E1 is satisfied, has an n-iteration Q-superlinear rate of convergence and a behaviour which is a precursor of every-iteration Q-superlinearity. This result overrides and corrects main result Theorem 3.1 of Ref. E1. © 1978 Plenum Publishing Corporation.