  The spectral theory of higher-order symmetric tensors is an important tool to
reveal some important properties of a hypergraph via its adjacency tensor,
Laplacian tensor, and signless Laplacian tensor. Owing to the sparsity of these
tensors, we propose an efficient approach to calculate products of these
tensors and any vectors. Using the state-of-the-art L-BFGS approach, we develop
a first-order optimization algorithm for computing H- and Z-eigenvalues of
these large scale sparse tensors (CEST). With the aid of the
Kurdyka-{\L}ojasiewicz property, we prove that the sequence of iterates
generated by CEST converges to an eigenvector of the tensor.When CEST is
started from multiple randomly initial points, the resulting best eigenvalue
could touch the extreme eigenvalue with a high probability. Finally, numerical
experiments on small hypergraphs show that CEST is efficient and promising.
Moreover, CEST is capable of computing eigenvalues of tensors corresponding to
a hypergraph with millions of vertices.
