Extrapolation methods for Pagerank computations

The mathematical problem behind Web search is the computation of the nonnegative left eigenvector of a stochastic matrix P corresponding to the dominant eigenvalue 1. This vector is called the PAGERANK vector. Since the matrix P is ill-conditioned, the computation of PAGERANK is difficult and the matrix P is replaced by P(c)=cP+(1-c)E, where E is a rank one matrix and c a parameter. The dominant left eigenvector of P(c) is denoted by PAGERANK(c). This vector can be computed for several values of c and then extrapolated at the point c=1. In this Note, we construct special extrapolation methods for this problem. They are based on the mathematical analysis of the vector PAGERANK(c).