Tensor norm and maximal singular vectors of non-negative tensors - a Perron-Frobenius theorem, a Collatz-Wielandt characterization and a generalized power method
Provides foundational theoretical results and an algorithmic approach for non-negative tensor singular value problems, which are important for multilinear algebra and data analysis.
The paper establishes a Perron-Frobenius theorem and Collatz-Wielandt characterization for the maximal singular value of non-negative tensors, and proposes a power method with asymptotic linear convergence for computing maximal singular vectors.
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.