New inertial factors of the Krasnosel’skiı̆-Mann iteration

We consider inertial iterative schemes for approximating a fixed point of any given non-expansive operator in real Hilbert spaces. We provide new conditions on the inertial factors that ensure weak convergence and depend only on the iteration coefficients. For the special case of the Douglas-Rachford splitting, the conditions boil down to a sufficiently small upper bound on the sequence of inertial factors. Rudimentary numerical results indicate practical usefulness of the proposal.