  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.
