Parallel multisplitting iteration methods based on M-splitting for the PageRank problem

A class of iterative schemes based on the regular splitting is proposed for PageRank computation. By some specific splitting, these methods will reduce to some well-known iterative schemes, like Jacobi method and successive overrelaxation method. To suit computational requirements of the modern high-speed multiprocessor environments, we further study synchronous parallel counterparts for the new splitting iteration methods. By using the M-splitting of the coefficient matrix, we establish the convergence theory of these synchronous multisplitting iteration methods. Finally, some numerical experiments are presented to illustrate the feasibility, stability and effectiveness of the proposed algorithms.