A General Framework for Iterative Aggregation/Disaggregation Methods

Aggregation/disaggregation methods are an important class of methods for computing the stationary probabilities of large-scale Markov chains. For Markov chains which are nearly uncoupled, iterative aggregation/disaggregation techniques can often result in sequences which converge at surprisingly rapid rates. But due to the variety of ways in which iterative aggregation/disaggregation methods are designed and implemented, it is generally necessary to analyze each algorithm in isolation, and it can be diicult to compare similarities and diierences. The purpose of this paper is to help overcome this situation by presenting a general framework for iterative aggregation/disaggregation algorithms which can be used to analyze and compare diierent and rather general algorithms from the class. We will demonstrate how several of the best known IAD algorithms t within this general framework.