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Application of an extrapolation method in the Hessenberg algorithm for computing PageRank

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Abstract

PageRank can be viewed as a hyperlink-based method for estimating the importance of nodes in a network, and has attracted a lot of attention from researchers. In this paper, we first propose an extrapolation procedure for PageRank vector estimation based on the linear combination of the Ritz values computed from the Hessenberg process and eigenvectors from the classical power method. In order to improve the convergence rate of the PageRank computations, the extrapolation procedure is introduced into the Hessenberg-type algorithm by Gu et al. (Numer. Algorithms, 89(4): 1845–1863, 2022), then a new algorithm is derived and named Hessenberg-extrapolation algorithm whose convergence and construction are investigated in detail. In addition, we further analyze the convergence of the Hessenberg-type algorithm and discuss the relationship between the approximate vectors of the Hessenberg-type algorithm and the Arnoldi-type algorithm. Numerical experiments on several examples demonstrate that our presented algorithm has great potential in PageRank approximation.

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Data Availability

The source code of our paper is available at https://github.com/smallmoon619/Hess-ext-PageRank.

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Funding

The work of the first author was supported by Scientific Research Project of the Guizhou Provincial Education (No. KY[2022]126). The second author was supported by Sichuan Science and Technology Program (No. 2022ZYD0006), Guanghua Talent Project of Southwestern University of Finance and Economics (Contract No. 20170224) and China Scholarship Council (Contract No. 202206985005).

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Authors and Affiliations

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

    Qian-Ying Hu

  2. School of Mathematics, Southwestern University of Finance and Economics, Chengdu, 611130, People’s Republic of China

    **an-Ming Gu

  3. School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu, 611731, People’s Republic of China

    Chun Wen

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  1. Qian-Ying Hu
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  2. **an-Ming Gu
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  3. Chun Wen
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Contributions

QYH contributed significantly to the conception of the study; QYH performed the experiment and wrote the manuscript; XMG and CW contributed significantly to analysis and manuscript preparation; CW helped perform the analysis with constructive discussions.

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Correspondence to **an-Ming Gu.

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Hu, QY., Gu, XM. & Wen, C. Application of an extrapolation method in the Hessenberg algorithm for computing PageRank. J Supercomput (2024). https://doi.org/10.1007/s11227-024-06327-y

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