  Large scale tensors, including large scale Hankel tensors, have many
applications in science and engineering. In this paper, we propose an inexact
curvilinear search optimization method to compute Z- and H-eigenvalues of $m$th
order $n$ dimensional Hankel tensors, where $n$ is large. Owing to the fast
Fourier transform, the computational cost of each iteration of the new method
is about $\mathcal{O}(mn\log(mn))$. Using the Cayley transform, we obtain an
effective curvilinear search scheme. Then, we show that every limiting point of
iterates generated by the new algorithm is an eigen-pair of Hankel tensors.
Without the assumption of a second-order sufficient condition, we analyze the
linear convergence rate of iterate sequence by the Kurdyka-{\L}ojasiewicz
property. Finally, numerical experiments for Hankel tensors, whose dimension
may up to one million, are reported to show the efficiency of the proposed
curvilinear search method.
