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An adaptively preconditioned multi-step matrix splitting iteration for computing PageRank

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Abstract

The multi-step matrix splitting iteration (MPIO) for computing PageRank is an efficient iterative method by combining the multi-step power method with the inner-outer iterative method. In this paper, with the aim of accelerating the computation of PageRank problems, a new method is proposed by preconditioning the MPIO method with an adaptive generalized Arnoldi (GArnoldi) method. The new method is called as an adaptive GArnoldi-MPIO method, whose construction and convergence analysis are discussed in detail. Numerical experiments on several PageRank problems are reported to illustrate the effectiveness of our proposed method.

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Acknowledgements

The authors would like to thank the anonymous referees for their valuable comments and suggestions on the original manuscript, which greatly improved the quality of this article.

Funding

This research is supported by the National Natural Science Foundation of China (12101433), and the Two-Way Support Programs of Sichuan Agricultural University (1921993077).

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Authors and Affiliations

  1. School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu, Sichuan, 610054, People’s Republic of China

    Chun Wen

  2. School of Mathematical Sciences, Guizhou Normal University, Guiyang, 550025, People’s Republic of China

    Qian-Ying Hu

  3. College of Science, Sichuan Agricultural University, Ya’an, Sichuan, 625000, People’s Republic of China

    Zhao-Li Shen

Authors
  1. Chun Wen
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  2. Qian-Ying Hu
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  3. Zhao-Li Shen
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Corresponding author

Correspondence to Chun Wen.

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The authors declare no competing interests.

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The datasets generated or analyzed during the current study are available from the corresponding author on reasonable request.

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Wen, C., Hu, QY. & Shen, ZL. An adaptively preconditioned multi-step matrix splitting iteration for computing PageRank. Numer Algor 92, 1213–1231 (2023). https://doi.org/10.1007/s11075-022-01337-4

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  • DOI: https://doi.org/10.1007/s11075-022-01337-4

Keywords

Mathematics Subject Classification (2010)