Iteration at Different Levels: Multi-Level Methods fro Structured Markov Chains

Abstract

For the stationary analysis of large Markov chains in continuous and discrete time a wide
variety of solution techniques has been applied in the past. Empirical
comparisons show that in particular so called multi-level approaches that
perform iterations at different levels are the most efficient 
solvers for a wide class of Markov chains. The methods combine ideas from
aggregation disaggregation methods and algebraic multigrid. 
The talk gives an overview of the basic ideas of multi level approaches and
shows which design alternatives for the algorithms exist. In particular it considers
different forms of defining levels,  available alternatives to realize
prolongation and interpolation operations, different cycle types and different
stopping criteria for the smoothing operations at each level. The last part of
the talk is devoted to implementation issues and data structures that are
necessary for an efficient realization of multi-level methods.