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).
Extrapolation methods for PageRank computations
SERRA CAPIZZANO, STEFANO
2005-01-01
Abstract
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).I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.