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A general multi-splitting iteration method for computing PageRank

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Abstract

In this paper, based on the multi-splitting iteration (MSI) method (Gu and Wang in J Appl Math Comput 42:479–490, 2013), we present a general multi-splitting iteration (GMSI) method for solving the PageRank problem. The convergence of the GMSI method is analyzed in detail. Moreover, the same idea can be used as a preconditioning technique to accelerate Krylov subspace methods, such as the GMRES method. Finally, several numerical examples are given to illustrate the effectiveness of the proposed algorithm.

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Notes

  1. This means neither \(N_{1}\) nor \(N_{2}-N_{1}\) is the null matrix.

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Acknowledgements

The corresponding author acknowledges the partial support of the China Scholarship Council (201706935029). We would like to thank Dr. P.H. Wen from Queen Mary University of London and Dr. Xiaoyan Liu from Taiyuan University of Technology for their valuable comments and suggestions, which improved the presentation of this paper.

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Authors and Affiliations

  1. Geomatics College, Shandong University of Science and Technology, Qingdao, 266590, People’s Republic of China

    Maoyi Tian & Yan Zhang

  2. College of Textile Engineering, Taiyuan University of Technology, Taiyuan, 030024, People’s Republic of China

    Yudong Wang

  3. College of Applied Mathematics, Shanxi University of Finance and Economics, Taiyuan, 030006, People’s Republic of China

    Zhaolu Tian

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  1. Maoyi Tian
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  2. Yan Zhang
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  3. Yudong Wang
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  4. Zhaolu Tian
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Correspondence to Zhaolu Tian.

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Communicated by Jinyun Yuan.

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Tian, M., Zhang, Y., Wang, Y. et al. A general multi-splitting iteration method for computing PageRank. Comp. Appl. Math. 38, 60 (2019). https://doi.org/10.1007/s40314-019-0830-8

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