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A continuation method for computing the multilinear PageRank
Author(s) -
Bucci Alberto,
Poloni Federico
Publication year - 2022
Publication title -
numerical linear algebra with applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.02
H-Index - 53
eISSN - 1099-1506
pISSN - 1070-5325
DOI - 10.1002/nla.2432
Subject(s) - multilinear map , pagerank , mathematics , continuation , extrapolation , computation , generalization , multilinear algebra , tensor (intrinsic definition) , representation (politics) , polynomial , mathematical optimization , algorithm , computer science , algebra over a field , mathematical analysis , pure mathematics , theoretical computer science , division algebra , politics , political science , law , filtered algebra , programming language
The multilinear PageRank model [Gleich et al., SIAM J Matrix Anal Appl , 2015;36(4):1507–41] is a tensor‐based generalization of the PageRank model. Its computation requires solving a system of polynomial equations that contains a parameter α ∈ [ 0 , 1 ) . For α ≈ 1 , this computation remains a challenging problem, especially since the solution may be nonunique. Extrapolation strategies that start from smaller values of α and “follow” the solution by slowly increasing this parameter have been suggested; however, there are known cases where these strategies fail, because a globally continuous solution curve cannot be defined as a function of α . In this article, we improve on this idea, by employing a predictor‐corrector continuation algorithm based on a more general representation of the solutions as a curve inℝ n + 1. We prove several global properties of this curve that ensure the good behavior of the algorithm, and we show in our numerical experiments that this method is significantly more reliable than the existing alternatives.