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Convergence of iterative aggregation/disaggregation methods based on splittings with cyclic iteration matrices

Iterative aggregation/disaggregation methods (IAD) belong to competitive tools for computation the characteristics of Markov chains as shown in some publications devoted to testing and comparing various methods designed to this purpose. According to Dayar T., Stewart W.J., ``Comparison of 
partitioning techniques for two-level iterative solvers on large, sparse Markov chains,'' SIAM J. Sci. Comput., Vol.21, No. 5, 1691-1705 (2000), the IAD methods are effective in particular when applied to large ill posed problems. One of the purposes of this 
paper is to contribute to a possible explanation of this fact. The 
novelty may consist of the fact that the IAD algorithms do converge independently of whether the iteration matrix of the corresponding process is primitive or not. Some numerical tests 
are presented and possible applications mentioned; e.g. computing the PageRank.