Arnoldi versus GMRES for computing pageRank: A theoretical contribution to google's pageRank problem

Authors:
Gang Wu;Yimin Wei
Affiliations:
Xuzhou Normal University;Fudan University, Shanghai
Venue:
ACM Transactions on Information Systems (TOIS)
Year:
2010

Citing 9
Cited 2

GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems

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On the Convergence of Restarted Krylov Subspace Methods

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Google's PageRank and Beyond: The Science of Search Engine Rankings

Google's PageRank and Beyond: The Science of Search Engine Rankings
Comparison of Krylov subspace methods on the PageRank problem

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On computing PageRank via lumping the Google matrix

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Ordinal Ranking for Google's PageRank

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An Arnoldi-Extrapolation algorithm for computing PageRank

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Lumping algorithms for computing Google's PageRank and its derivative, with attention to unreferenced nodes

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Accelerating the Arnoldi-Type Algorithm for the PageRank Problem and the ProteinRank Problem

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Abstract

PageRank is one of the most important ranking techniques used in today's search engines. A recent very interesting research track focuses on exploiting efficient numerical methods to speed up the computation of PageRank, among which the Arnoldi-type algorithm and the GMRES algorithm are competitive candidates. In essence, the former deals with the PageRank problem from an eigenproblem, while the latter from a linear system, point of view. However, there is little known about the relations between the two approaches for PageRank. In this article, we focus on a theoretical and numerical comparison of the two approaches. Numerical experiments illustrate the effectiveness of our theoretical results.