Aggregation/disaggregation as a theoretical tool

  • Ivo Marek Czech Institute of Technology
Keywords: stationary probability vector of a Markov chain, iterative aggregation/disaggregation, Google matrix


The main aim of this contribution is to establish convergence of some iterative procedures that play an important role in the PageRank computation. The problems we are interested in are considered in two recent papers by Ipsen and Selee, and Lee, Golub and
Zenios. Both these papers present new ideas to solve the celebrated problem of the PageRank. Our aim is to show that the results and some generalizations of them can be proven via an application of the iterative aggregation/disaggregation methods. One of the results may be of particular interest. It concerns a proof that the two-stage algorithm proposed by Lee, Golub and Zenios does compute the PageRank. This problem has been raised in the literature. We answer this question in positive by showing appropriate necessary and sufficient conditions. In addition a short proof of the celebrated Google lemma is presented.


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