A note on the two-step matrix splitting iteration for computing PageRank

Computing PageRank plays an important part in determining the importance of Web pages. Based on the classical power method and the inner-outer iteration proposed by Gleich et al. (2010), Gu et al. (2015) presented a two-step splitting iteration, i.e., the power-inner-outer (PIO) iteration, for the computation of PageRank. In this paper, we develop a variant of the PIO iteration by applying multi-step power method to combine with the inner-outer iteration. The new method is denoted as the MPIO iteration, its convergence is analyzed in detail. Numerical experiments on several PageRank problems are used to illustrate the effectiveness of the MPIO iteration.