We present a simple automatic over-correction
mechanism to accelerate multilevel aggregation methods for
the computation of the stationary probability vector of irreducible
Markov chains. Over-correction is motivated by the observation
that while the correction typically approximates the error
very well in the sense of its ``direction'', it may not provide
a good approximation in the sense of its ``size'' [Vanek and
Míka, 1992]. In the case of a multiplicative correction scheme,
which is commonly used for Markov chains, each component of the
correction is exponentiated by a small factor
, that is
recalculated on each level. Applying the over-correction in this way has
the added benefit of maintaining positivity of the correction. Numerical
experiments demonstrate that this
approach can lead to significant speedup of basic multilevel
aggregation for Markov chains, at little extra cost.