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On the multi-splitting iteration method for computing PageRank

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Abstract

A two-step iterative scheme based on the multiplicative splitting iteration is presented for PageRank computation. The new algorithm is applied to the linear system formulation of the problem. Our method is essentially a two-parameter iteration which can extend the possibility to optimize the iterative process. Theoretical analyses show that the iterative sequence produced by our method is convergent to the unique solution of the linear system, i.e., PageRank vector. An exact parameter region of convergence for the method is strictly proved. In each iteration, the proposed method requires solving two linear sub-systems with the splitting of the coefficient matrix of the problem. We consider using inner iterations to compute approximate solutions of these linear sub-systems. Numerical examples are presented to illustrate the efficiency of the new algorithm.

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Notes

  1. Here and in what follows, A=M−N is called a splitting of the matrix A if M is a nonsingular matrix.

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Acknowledgements

The authors would like to thank the anonymous referees for their valuable comments and suggestion on the original manuscript. These brought several enhancements to our initial work.

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Authors and Affiliations

  1. Department of Mathematics, Shanghai University, Shanghai, 200444, China

    Chuanqing Gu & Lei Wang

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  1. Chuanqing Gu
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  2. Lei Wang
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Correspondence to Chuanqing Gu.

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The work are supported by Shanghai Natural Science Foundation (10ZR1410900), Key Disciplines of Shanghai Municipality (S30104), Innovation Program of Shanghai Municipal Education Commission (13ZZ068), Natural Science Foundation of Universities of Anhui Province (KJ2011A248, KJ2012Z347) and Young Foundation of Huaibei Normal University (700583).

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Gu, C., Wang, L. On the multi-splitting iteration method for computing PageRank. J. Appl. Math. Comput. 42, 479–490 (2013). https://doi.org/10.1007/s12190-013-0645-5

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