Acceleration of the generalized FOM algorithm for computing PageRank

In this paper, a generalized full orthogonalization method (GFOM) based on weighted inner products is discussed for computing PageRank. In order to improve convergence performance, the GFOM algorithm is accelerated by two cheap methods respectively, one is the power method and the other is the extrapolation method based on Ritz values. Such that two new algorithms called GFOM-Power and GFOM-Extrapolation are proposed for computing PageRank. Their implementations and convergence analyses are studied in detail. Numerical experiments are used to show the efficiency of our proposed algorithms.