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The purpose of the paper is to present some convergence properties of the iterative aggregation–disaggregation method for computing a stationary probability distribution vector of a column stochastic matrix.
A sufficient condition for the local convergence property and the corresponding rate of convergence are established.
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Computing Google’s Page Rank via lumping the Google matrix was recently analyzed in [I.
In this note, we show that the reduced matrix obtained by lumping the dangling nodes can be further reduced by lumping a class of nondangling nodes, called weakly nondangling nodes, to another single node, and the further reduced matrix is also stochastic with the same nonzero eigenvalues as the Google matrix.
It was shown that all of the dangling nodes can be lumped into a single node and the Page Rank could be obtained by applying the power method to the reduced matrix.