  We study the l^{p_1,...,p_m} singular value problem for non-negative tensors.
We prove a general Perron-Frobenius theorem for weakly irreducible and
irreducible nonnegative tensors and provide a Collatz-Wielandt characterization
of the maximal singular value. Additionally, we propose a higher order power
method for the computation of the maximal singular vectors and show that it has
an asymptotic linear convergence rate.
