===affil2:
University of Waterloo
===firstname:
Killian, L
===firstname4:
Irad
===firstname3:
Eran
===lastname2:
De Sterck
===lastname:
Miller
===firstname5:

===affil6:

===lastname3:
Treister
===email:
killianmiller@gmail.com
===lastname6:

===affil5:

===otherauths:

===lastname4:
Yavneh
===affil4:
Israel institute for technology - Technion
===lastname7:

===affil7:

===firstname7:

===postal:
Department of Applied Mathematics
University of Waterloo
Waterloo, Ontario, N2L 3G1
Canada

===firstname6:

===ABSTRACT:
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 coarse-grid 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'' [Van\v{e}k and
M\'{i}ka, 1992]. In the case of a multiplicative correction scheme,
which is commonly used for Markov chains, we apply the
over-correction technique via componentwise exponentiation
of the correction by a small factor $\alpha > 1$, that is recalculated
on each level. Numerical experiments demonstrate that this
approach can lead to significant speedup of basic multilevel
aggregation for Markov chains, at little extra cost.
===affil3:
Israel institute for technology - Technion
===lastname5:

===affilother:

===title:
Over-correction for multilevel aggregation for Markov chains
===firstname2:
Hans