ON THE EFFECTS OF USING THE GRASSMANN-TAKSAR-HEYMAN METHOD IN ITERATIVE AGGREGATION-DISAGGREGATION

Iterative aggregation-disaggregation (IAD) is an effective method for solving finite nearly completely decomposable (NCD) Markov chains. Sma ll perturbations in the transition probabilities of these chains may l ead to considerable changes in the stationary probabilities; NCD Marko v chains are known to be ill-conditioned. During an IAD step, this und esirable condition is inherited by the coupling matrix arid one confro nts the problem of finding the stationary probabilities of a stochasti c matrix whose diagonal elements are close to 1. Tn this paper, the ef fects of using the Grassmann-Taksar-Heyman (GTH) method to solve the c oupling matrix formed in the aggregation step are investigated. Then t he idea is extended in such a way that the same direct method can be i ncorporated into the disaggregation step. Finally, the effects of usin g the GTH method in the IAD algorithm on various examples are demonstr ated, and the conditions under which it should be employed are explain ed.