Behaviour in the limit of iterations of the stochastic two-step method

An algorithm which can be regarded as a stochastic analogue of the conjugate gradients method or of the heavy-sphere method is studied. The asymptotic properties of the method, and of the stochastic analogue of the gradient method, are compared. It is shown that, in certain cases, the former method is no worse than the latter method, in the sense of the systematic asymptotic displacement from the minimum point.