  Some methods for the convergence acceleration of the M{\o}ller-Plesset
perturbation series for the correlation energy are discussed. The
order-by-order summation is less effective than the Feenberg series. The latter
is obtained by renormalizing the unperturbed Hamilton operator by a constant
factor that is optimized for the third order energy. In the fifth order case,
the Feenberg series can be improved by order-dependent optimization of the
parameter. Alternatively, one may use Pad{\'e} approximants or a further method
based on effective characteristic polynomials to accelerate the convergence of
the perturbation series. Numerical evidence is presented that, besides the
Feenberg-type approaches, suitable Pad{\'e} approximants, and also the
effective second order characteristic polynomial, are excellent tools for
correlation energy estimation.
