Tensor norm and maximal singular vectors of non-negative tensors - a Perron-Frobenius theorem, a Collatz-Wielandt characterization and a generalized power method

摘要

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 andirreducible nonnegative tensors and provide a Collatz-Wielandt characterizationof the maximal singular value. Additionally, we propose a higher order powermethod for the computation of the maximal singular vectors and show that it hasan asymptotic linear convergence rate.