  The Perron-Frobenius theorem says that the spectral radius of an irreducible
nonnegative tensor is the unique positive eigenvalue corresponding to a
positive eigenvector. With this in mind, the purpose of this paper is to find
the spectral radius and its corresponding positive eigenvector of an
irreducible nonnegative symmetric tensor. By transferring the eigenvalue
problem into an equivalent problem of minimizing a concave function on a closed
convex set, which is typically a DC (difference of convex functions)
programming, we derive a simpler and cheaper iterative method. The proposed
method is well-defined. Furthermore, we show that both sequences of the
eigenvalue estimates and the eigenvector evaluations generated by the method
$Q$-linearly converge to the spectral radius and its corresponding eigenvector,
respectively. To accelerate the method, we introduce a line search technique.
The improved method retains the same convergence property as the original
version. Preliminary numerical results show that the improved method performs
quite well.
