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

REDIVO ZAGLIA, MICHELA;
2005

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).
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11577/1426552
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