  In this paper we analyse convergence of projected fixed-point iteration on a
Riemannian manifold of matrices with fixed rank. As a retraction method we use
`projector splitting scheme'. We prove that the projector splitting scheme
converges at least with the same rate as standard fixed-point iteration without
rank constraints. We also provide counter-example to the case when conditions
of the theorem do not hold. Finally we support our theoretical results with
numerical experiments.
