The multilinear Pagerank model [Gleich, Lim and Yu, 2015] is a tensor-based generalization of the Pagerank model. Its computation requires solving a system of polynomial equations that contains a parameter $\alpha \in [0,1)$. For $\alpha \approx 1$, this computation remains a challenging problem, especially since the solution may be non-unique. Extrapolation strategies that start from smaller values of $\alpha$ 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 $\alpha$. In this paper, we improve on this idea, by employing a predictor-corrector continuation algorithm based on a more general representation of the solutions as a curve in $\mathbb{R}^{n+1}$. 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.

中文翻译：

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计算多线性Pagerank的一种连续方法

多线性Pagerank模型[Gleich，Lim and Yu，2015]是Pagerank模型的基于张量的泛化。它的计算需要求解一个包含参数$ \ alpha \ in [0,1）$的多项式方程组。对于$ \ alpha \ approx 1 $，此计算仍然是一个具有挑战性的问题，尤其是因为解可能是不唯一的。已经提出了从$ \ alpha $的较小值开始并通过缓慢增加此参数来“跟随”解决方案的外推策略；但是，在某些情况下，这些策略会失败，因为无法将全局连续解曲线定义为$ \ alpha $的函数。在本文中，我们通过采用基于解决方案的更一般表示形式的预测器-校正器连续算法作为$ \ mathbb {R} ^ {n + 1} $中的曲线，对这一思想进行了改进。