A Power–Arnoldi algorithm for computing PageRank

Abstract The PageRank algorithm plays an important role in modern search engine technology. It involves using the classical power method to compute the principle eigenvector of the Google matrix representing the web link graph. However, when the largest eigenvalue is not well separated from the second one, the power method may perform poorly. This happens when the damping factor is sufficiently close to 1. Therefore, it is worth developing new techniques that are more sophisticated than the power method. The approach presented here, called Power–Arnoldi, is based on a periodic combination of the power method with the thick restarted Arnoldi algorithm. The justification for this new approach is presented. Numerical tests illustrate the efficiency and convergence behaviour of the new algorithm. Copyright © 2007 John Wiley & Sons, Ltd.