Jordan Canonical Form of the Google Matrix: A Potential Contribution to the PageRank Computation

Authors:
Stefano Serra-Capizzano
Affiliations:
-
Venue:
SIAM Journal on Matrix Analysis and Applications
Year:
2005

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Abstract

We consider the web hyperlink matrix used by Google for computing the PageRank whose form is given by A(c)=[cP +(1-c)E]T, where P is a row stochastic matrix, E is a row stochastic rank one matrix, and $c\in [0,1]$. We determine the analytic expression of the Jordan form of A(c) and, in particular, a rational formula for the PageRank in terms of c. The use of extrapolation procedures is very promising for the efficient computation of the PageRank when c is close or equal to 1.