  The Krasnosel'skii-Mann (KM) algorithm is the most fundamental iterative
scheme designed to find a fixed point of an averaged operator in the framework
of a real Hilbert space, since it lies at the heart of various numerical
algorithms for solving monotone inclusions and convex optimization problems. We
enhance the Krasnosel'skii-Mann algorithm with Nesterov's momentum updates and
show that the resulting numerical method exhibits a convergence rate for the
fixed point residual of $o(1/k)$ while preserving the weak convergence of the
iterates to a fixed point of the operator. Numerical experiments illustrate the
superiority of the resulting so-called Fast KM algorithm over various fixed
point iterative schemes, and also its oscillatory behavior, which is a specific
of Nesterov's momentum optimization algorithms.
