A general multi-step matrix splitting iteration method for computing PageRank

Abstract

Computing PageRank vector is very important in determining the importance of web pages. By combining multi-step power method with the inner-outer (IO) iteration [24], Wen et al. [6] proposed the multi-step power-inner-outer (MPIO) iteration method. Based on the general innerouter (GIO) iteration method [5,34] and the iteration framework [6], we present a general multistep matrix splitting (GMMS) iteration method in this paper, and analyze its overall convergence property. Moreover, the same idea can be used as a preconditioning technique for accelerating the Krylov subspace methods, such as GMRES method. Finally, several numerical examples are given to illustrate the effectiveness of the proposed algorithm.