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Efficient numerical methods to solve sparse linear equations with application to PageRank

Author

Listed:
  • Anikin, A.
  • Gasnikov, A.
  • Gornov, A.
  • Kamzolov, D.
  • Maximov, Y.
  • Nesterov, Yurii

    (Université catholique de Louvain, LIDAM/CORE, Belgium)

Abstract

Over the last two decades, the PageRank problem has received increased interest from the academic community as an efficient tool to estimate web-page importance in information retrieval. Despite numerous developments, the design of efficient optimization algorithms for the PageRank problem is still a challenge. This paper proposes three new algorithms with a linear time complexity for solving the problem over a bounded-degree graph. The idea behind them is to set up the PageRank as a convex minimization problem over a unit simplex, and then solve it using iterative methods with small iteration complexity. Our theoretical results are supported by an extensive empirical justification using real-world and simulated data.

Suggested Citation

  • Anikin, A. & Gasnikov, A. & Gornov, A. & Kamzolov, D. & Maximov, Y. & Nesterov, Yurii, 2023. "Efficient numerical methods to solve sparse linear equations with application to PageRank," LIDAM Reprints CORE 3232, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    • Handle: RePEc:cor:louvrp:3232
    DOI: https://doi.org/10.1080/10556788.2020.1858297
    Note: In: Optimization Methods and Software, 2022, vol. 37(3), p. 907-935
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