An Arnoldi-Extrapolation algorithm for computing PageRank

Authors:
Gang Wu;Yimin Wei
Affiliations:
School of Mathematical Sciences, Xuzhou Normal University, Xuzhou, 221116, Jiangsu, PR China;School of Mathematical Sciences, Fudan University, Shanghai, 200433, PR China and Shanghai Key Laboratory of Contemporary Applied Mathematics, PR China
Venue:
Journal of Computational and Applied Mathematics
Year:
2010

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Abstract

The Arnoldi-type algorithm proposed by Golub and Greif [G. Golub, C. Greif, An Arnoldi-type algorithm for computing PageRank, BIT 46 (2006) 759-771] is a restarted Krylov subspace method for computing PageRank. However, this algorithm may not be efficient when the damping factor is high and the dimension of the search subspace is small. In this paper, we first develop an extrapolation method based on Ritz values. We then consider how to periodically knit this extrapolation method together with the Arnoldi-type algorithm. The resulting algorithm is the Arnoldi-Extrapolation algorithm. The convergence of the new algorithm is analyzed. Numerical experiments demonstrate the numerical behavior of this algorithm.