  Folklore says that Howard's Policy Improvement Algorithm converges
extraordinarily fast, even for controlled diffusion settings.
  In a previous paper, we proved that approximations of the solution of a
particular parabolic partial differential equation obtained via the policy
improvement algorithm show a quadratic local convergence.
  In this paper, we show that we obtain the same rate of convergence of the
algorithm in a more general setup. This provides some explanation as to why the
algorithm converges fast.
  We provide an example by solving a semilinear elliptic partial differential
equation numerically by applying the algorithm and check how the approximations
converge to the analytic solution.
