Abstract
SUMMARYWe 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.
Published Version
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