  Higher-order Markov chains play a very important role in many fields, ranging
from multilinear PageRank to financial modeling. In this paper, we propose
three accelerated higher-order power methods for computing the limiting
probability distribution of higher-order Markov chains, namely higher-order
power method with momentum and higher-order quadratic extrapolation method. The
convergence results are established, and numerical experiments are reported to
show the efficiency of the proposed algorithms. In particular, the
non-parametric quadratic extrapolation method is very competitive, and
outperforms state-of-the-art competitions.
