The Finest Level Acceleration of Multilevel Aggregation for Markov Chains

In this paper, we consider a class of new accelerated multilevel aggregation methods using two polynomial-type vector extrapolation methods, namely the reduced rank extrapolation (RRE) and the generalization of quadratic extrapolation (GQE) methods. We show how to combine the multilevel aggregation methods with the RRE and GQE algorithms on the finest level in order to speed up the numerical computation of the stationary probability vector for an irreducible Markov chain. Numerical experiments on typical Markov chain problems are reported to illustrate the efficiency of the accelerated multilevel aggregation methods.