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arXiv · 1503.01273

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

Antoine Gautier·Matthias Hein
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Abstract

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.

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Antoine Gautier, Matthias Hein. 2015-03-04. Tensor norm and maximal singular vectors of non-negative tensors - a Perron-Frobenius theorem, a Collatz-Wielandt characterization and a generalized power method. https://arxiv.org/abs/1503.01273

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