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

2015/03/04 by Antoine Gautier, Matthias Hein, Gautier, Antoine +1
Mathematics · #15A48 #47H07 #47H09 #47H10 #Benford’s Law and Fraud Detection #FOS: Mathematics #Mathematical Approximation and Integration #Numerical Analysis (math.NA) #Spectral Theory (math.SP) #Tensor decomposition and applications

paper · pdf · doi:10.48550/arxiv.1503.01273

openalex publication_date 2015/03/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the l^p₁,...,p_m singular value problem for non-negative tensors.\nWe prove a general Perron-Frobenius theorem for weakly irreducible and\nirreducible nonnegative tensors and provide a Collatz-Wielandt characterization\nof the maximal singular value. Additionally, we propose a higher order power\nmethod for the computation of the maximal singular vectors and show that it has\nan asymptotic linear convergence rate.\n

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