This paper by Sepandar Kamvar, Taher Haveliwala, and Gene Golub describes an algorithm to speed up the computation of PageRank using the fact that pages converge at different rates.
Abstract, slide show, references, from First Steps on the Road to Reinventing Computing, by Ian Piumarta, Viewpoints Research Institute. Stanford EE Computer Systems Colloquium, 2007 Feb 14.
PhD thesis by Kahn Mason on methods of discovering groups of websites that collude to boost their reputations, distorting the results of the PageRank algorithm. Stanford University.
This paper by Sepandar Kamvar, Taher Haveliwala, Chris Manning, and Gene Golub, published in WWW13, presents an algorithm to speed up the computation of PageRank by making some initial approximations.
A paper about the computation of PageRank using the standard Power Method and the new Quadratic Extrapolation which computes the principal eigenvector of the Markov matrix representing the Web link graph with an increased speed up of about 50-300%.