NEW POSSIBILITIES REGARDING THE ALTERNATING PROJECTIONS METHOD - Pustylnik, E.; Reich, S.; Zaslavski, A. J. (Journal of Nonlinear Analysis and Optimization: Theory & Applications (JNAO), 2011)
We provide a short survey of some recent results of ours regarding the convergence of infinite products of nonexpansive operators, some of which are orthogonal projections, while others may even be nonlinear. It turns out that the standard requirement of cyclic order of the projections may be replaced with the positivity of the angles between the given subspaces. Moreover, one of these angles may even be unknown, provided the corresponding projection appears in the infinite product sufficiently rarely.