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2012, 2(4): 855-862. doi: 10.3934/naco.2012.2.855

## On convergence of the inner-outer iteration method for computing PageRank

 1 School of Mathematics and Computer Science, Guizhou Normal University, Guiyang 550001, China

Received  January 2012 Revised  October 2012 Published  November 2012

Without imposing any restriction on the damping factors and the stopping tolerances, we prove the overall convergence of the inner-outer iteration method for computing the PageRank vector, which was proposed by Gleich, Gray, Greif and Lau (SIAM J. Sci. Comput. 32(2010)349-371). Based on the formula of the contraction factor of the method, we discuss possible choices of the iteration parameters, which could be practically useful for accelerating the convergence rate of the inner-outer iteration method.
Citation: Zhong-Zhi Bai. On convergence of the inner-outer iteration method for computing PageRank. Numerical Algebra, Control & Optimization, 2012, 2 (4) : 855-862. doi: 10.3934/naco.2012.2.855
##### References:
 [1] Z. -Z. Bai, J. -C. Sun and D. -R. Wang, A unified framework for the construction of various matrix multisplitting iterative methods for large sparse system of linear equations,, Computers Math. Appl., 32 (1996), 51.  doi: 10.1016/S0898-1221(96)00207-6.  Google Scholar [2] P. Berkhin, A survey on PageRank computing,, Internet Math., 2 (2005), 73.  doi: 10.1080/15427951.2005.10129098.  Google Scholar [3] A. N. Langville and C. D. Meyer, A survey of eigenvector methods for Web information retrieval,, SIAM Rev., 47 (2005), 135.  doi: 10.1137/S0036144503424786.  Google Scholar [4] L. Page, S. Brin, R. Motwani and T. Winograd, "The PageRank Citation Ranking: Bringing Order to the Web,", Stanford Digital Libraries SIDL-WP-1999-0120, (1999), 1999.   Google Scholar [5] D. F. Gleich, A. P. Gray, C. Greif and T. Lau, An inner-outer iteration for computing PageRank,, SIAM J. Sci. Comput., 32 (2010), 349.  doi: 10.1137/080727397.  Google Scholar [6] J. -F. Yin, G. -J. Yin and M. K. Ng, On adaptively accelerated Arnoldi method for computing PageRank,, Numer. Linear Algebra Appl., 19 (2012), 73.  doi: 10.1002/nla.789.  Google Scholar

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##### References:
 [1] Z. -Z. Bai, J. -C. Sun and D. -R. Wang, A unified framework for the construction of various matrix multisplitting iterative methods for large sparse system of linear equations,, Computers Math. Appl., 32 (1996), 51.  doi: 10.1016/S0898-1221(96)00207-6.  Google Scholar [2] P. Berkhin, A survey on PageRank computing,, Internet Math., 2 (2005), 73.  doi: 10.1080/15427951.2005.10129098.  Google Scholar [3] A. N. Langville and C. D. Meyer, A survey of eigenvector methods for Web information retrieval,, SIAM Rev., 47 (2005), 135.  doi: 10.1137/S0036144503424786.  Google Scholar [4] L. Page, S. Brin, R. Motwani and T. Winograd, "The PageRank Citation Ranking: Bringing Order to the Web,", Stanford Digital Libraries SIDL-WP-1999-0120, (1999), 1999.   Google Scholar [5] D. F. Gleich, A. P. Gray, C. Greif and T. Lau, An inner-outer iteration for computing PageRank,, SIAM J. Sci. Comput., 32 (2010), 349.  doi: 10.1137/080727397.  Google Scholar [6] J. -F. Yin, G. -J. Yin and M. K. Ng, On adaptively accelerated Arnoldi method for computing PageRank,, Numer. Linear Algebra Appl., 19 (2012), 73.  doi: 10.1002/nla.789.  Google Scholar
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