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

DOI10.1016/j.laa.2016.04.024zbMath1360.15029arXiv1503.01273OpenAlexW2964185177MaRDI QIDQ290680

Matthias Hein, Gautier, Antoine

Publication date: 3 June 2016

Published in: Linear Algebra and its Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1503.01273

zbMATH Keywords

convergence analysis of the higher order power methodmaximal singular valuePerron-Frobenius theorem for nonnegative tensors

Mathematics Subject Classification ID

Fixed-point theorems (47H10) Contraction-type mappings, nonexpansive mappings, (A)-proper mappings, etc. (47H09) Positive matrices and their generalizations; cones of matrices (15B48) Monotone and positive operators on ordered Banach spaces or other ordered topological vector spaces (47H07) Multilinear algebra, tensor calculus (15A69)

Related Items (7)

Newton Correction Methods for Computing Real Eigenpairs of Symmetric Tensors ⋮ Eigenvalues of the solution of the Lyapunov tensor equation ⋮ Nonlinear Perron--Frobenius Theorems for Nonnegative Tensors ⋮ The global convergence of the nonlinear power method for mixed-subordinate matrix norms ⋮ Dynamical properties of endomorphisms, multiresolutions, similarity and orthogonality relations ⋮ The Perron--Frobenius Theorem for Multihomogeneous Mappings ⋮ A Unifying Perron--Frobenius Theorem for Nonnegative Tensors via Multihomogeneous Maps

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