A preconditioned and extrapolation-accelerated GMRES method for PageRank

In this paper, we propose and analyze GMRES-type methods for the PageRank computation. However, GMRES may converge very slowly or sometimes even diverge or break down when the damping factor is close to 1 and the dimension of the search subspace is low. We propose two strategies: preconditioning and vector extrapolation accelerating, to improve the convergence rate of the GMRES method. Theoretical analysis demonstrate the efficiency of the proposed strategies and numerical experiments show that the performance of the proposed methods is very much better than that of the traditional methods for PageRank problems.