On convergence of the inner-outer iteration method for computing PageRank

Without imposing any restriction on the damping factors andthe stopping tolerances, we prove the overall convergenceof the inner-outer iteration method for computingthe PageRank vector, which was proposed byGleich, Gray, Greif and Lau (SIAM J. Sci. Comput. 32(2010)349-371).Based on the formula of the contraction factor of the method,we discuss possible choices of the iteration parameters,which could be practically useful for accelerating theconvergence rate of the inner-outer iteration method.