  Nesterov's well-known scheme for accelerating gradient descent in convex
optimization problems is adapted to accelerating stationary iterative solvers
for linear systems. Compared with classical Krylov subspace acceleration
methods, the proposed scheme requires more iterations, but it is trivial to
implement and retains essentially the same computational cost as the
unaccelerated method. An explicit formula for a fixed optimal parameter is
derived in the case where the stationary iteration matrix has only real
eigenvalues, based only on the smallest and largest eigenvalues. The fixed
parameter, and corresponding convergence factor, are shown to maintain their
optimality when the iteration matrix also has complex eigenvalues that are
contained within an explicitly defined disk in the complex plane. A comparison
to Chebyshev acceleration based on the same information of the smallest and
largest real eigenvalues (dubbed Restricted Information Chebyshev acceleration)
demonstrates that Nesterov's scheme is more robust in the sense that it remains
optimal over a larger domain when the iteration matrix does have some complex
eigenvalues. Numerical tests validate the efficiency of the proposed scheme.
This work generalizes and extends the results of [1, Lemmas 3.1 and 3.2 and
Theorem 3.3].
