Jordan Canonical Form of the Google Matrix: A Potential Contribution to the PageRank Computation
Stefano Serra‐Capizzano · SIAM Journal on Matrix Analysis and Applications · 2005
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.