Anderson accelerated fixed‐point iteration for multilinear PageRank

Abstract

In this paper, we apply the Anderson acceleration technique to the existing relaxation fixed‐point iteration for solving the multilinear PageRank. In order to reduce computational cost, we further consider the periodical version of the Anderson acceleration. The convergence of the proposed algorithms is discussed. Numerical experiments on synthetic and real‐world datasets are performed to demonstrate the advantages of the proposed algorithms over the relaxation fixed‐point iteration and the extrapolated shifted fixed‐point method. In particular, we give a strategy for choosing the quasi‐optimal parameters of the associated algorithms when they are applied to solve the test problems with different sizes but the same structure.