A two-step matrix splitting iteration for computing PageRank

The PageRank algorithm plays an important role in determining the importance of Web pages. The core of this algorithm involves using the classical power method to compute the PageRank vector, which is the principal eigenvector of the matrix representing the Web link graph. Nevertheless, it is well known that the power method may perform poorly when the second largest eigenvalue is close to the dominant one. In this article, we present a new approach that is based on the two-step splitting iteration framework. The description and convergence of the new algorithm are discussed in detail. Numerical examples are given to illustrate the performance of this algorithm.