A preprocessed multi-step splitting iteration for computing PageRank

The PageRank algorithm plays an important role in determining the importance of Web pages. The multi-step splitting iteration (MSPI) method for calculating the Pagerank problem is an iterative framework of combining the multi-step classical power method with the inner-outer method. In this paper, we present a preprocessed MSPI method called the Arnoldi-MSPI iteration, which is the MSPI method modified with the thick restarted Arnoldi algorithm. The implementation and convergence of the new method are discussed in detail. Numerical experiments are given to show that our method has a good computational effect when the damping factor is close to 1.