Physiology and pathology of iterative aggregation-disaggregation methods

SUMMARY We found characteristics that can help us predict the convergence or divergence of iterative aggregation–disaggregation methods. We provided two results for spectral radii of asymptotic error propagation matrices: (i) the spectral radius is bounded by unity for symmetric Markov chains and (ii) the spectral radius can be arbitrarily large for a certain class of sparse Markov chains. Surprisingly, permuting states of cyclic Markov chains by algorithms usually used for reducing bandwidth of matrices leads to the latter case. We proposed a sorting method that prevents divergence for this class of Markov chains.Copyright © 2011 John Wiley & Sons, Ltd.

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