Accelerating the Arnoldi-Type Algorithm for the PageRank Problem and the ProteinRank Problem

PageRank is an algorithm for computing a ranking for every Web page based on the graph of the Web. It plays an important role in Google's search engine. The core of the PageRank algorithm involves computing the principal eigenvector of the Google matrix. Currently, we need to solve PageRank problems with high damping factors, which cost considerable time. A possible approach for accelerating the computation is the Arnoldi-type algorithm. However, this algorithm may not be satisfactory when the damping factor is high and the dimension of the Krylov subspace is low. Even worse, it may stagnate in practice. In this paper, we propose two strategies to improve the efficiency of the Arnoldi-type algorithm. Theoretical analysis shows that the new algorithms can accelerate the original Arnoldi-type algorithm considerably, and circumvent the drawback of stagnation. Numerical experiments illustrate that the accelerated Arnoldi-type algorithms usually outperform many state-of-the-art accelerating algorithms for PageRank. Applications of the new algorithms to function predicting of proteins are also discussed.