Convergence Analysis of an Improved Pagerank Algorithm

The iterative aggregation/disaggregation (IAD) method is an improvement of the PageRank algorithm used by the search engine Google to compute stationary probabilities of very large Markov chains. In this paper the convergence, in exact arithmetic, of the IAD method is analyzed. The IAD method is expressed as the power method preconditioned by an incomplete LU factorization. This leads to a simple derivation of the asymptotic convergence rate of the IAD method. It is shown that the power method applied to the Google matrix always converges, and that the convergence rate of the IAD method is at least as good as that of the power method. Furthermore, by exploiting the hyperlink structure of the web it can be shown that the convergence rate of the IAD method applied to the Google matrix can be made strictly faster than that of the power method.