A continuation method for computing the multilinear PageRank

The multilinear PageRank model [Gleich et al., SIAM J Matrix Anal Appl, 2015;36(4):1507–41] is a tensor-based generalization of the model. Its computation requires solving system polynomial equations that contains parameter ? ? [ 0 , 1 ) . For ? this remains challenging problem, especially since solution may be nonunique. Extrapolation strategies start from smaller values and “follow” by slowly increasing have been suggested; however, there are known cases where these fail, because globally continuous curve cannot defined as function In article, we improve on idea, employing predictor-corrector continuation algorithm based more general representation solutions in ? n + We prove several global properties ensure good behavior algorithm, show our numerical experiments method significantly reliable than existing alternatives.