The general inner-outer iteration method based on regular splittings for the PageRank problem

Abstract

In this paper, combined the regular splittings of the coefficient matrix I−αP with the inner-outer iteration framework [9], a general inner-outer (GIO) iteration method is presented for solving the PageRank problem. Firstly, the AOR and modified AOR (MAOR) methods for solving the PageRank problem are constructed, and several comparison results are also given. Next, the GIO iteration scheme is developed, and its overall convergence is analyzed in detail. Furthermore, the preconditioner derived from the GIO iteration can be used to accelerate the Krylov subspace methods, such as GMRES method. Finally, some numerical experiments on several PageRank problems are provided to illustrate the efficiency of the proposed algorithm.