A simpler GMRES algorithm accelerated by Chebyshev polynomials for computing PageRank

Abstract

PageRank is one of the most important ranking techniques in modern search engines. Many great interesting researches focus on developing efficient numerical methods to compute PageRank problems. In this paper, we consider a simpler generalized minimal residual (SGMRES) algorithm for computing PageRank. The main features of the SGMRES algorithm lie in that there is no need to factorize an upper Hessenberg matrix, and the residual vector is easily obtained at each iteration. To speed up the computation of PageRank problems, an accelerated technique based on Chebyshev polynomials is applied to improve the SGMRES algorithm, such that a new algorithm named SGMRES-Chebyshev is proposed here. The implementation and the convergence analysis of the new algorithm are discussed in detail. Numerical experiments are used to illustrate the efficiency of our proposed algorithm.