On Orthogonal Tensors and Best Rank-One Approximation Ratio

DOI10.1137/17M1144349zbMath1390.15081arXiv1707.02569OpenAlexW2963542075WikidataQ114074316 ScholiaQ114074316MaRDI QIDQ5373918

Tasuku Soma, André Uschmajew, Yuji Nakatsukasa, Zhening Li

Publication date: 6 April 2018

Published in: SIAM Journal on Matrix Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1707.02569

zbMATH Keywords

Hurwitz problemspectral normnuclear normorthogonal tensorrank-one approximation

Mathematics Subject Classification ID

Norms of matrices, numerical range, applications of functional analysis to matrix theory (15A60) Multilinear algebra, tensor calculus (15A69) Composition algebras (17A75)

Related Items (17)

New estimations on the upper bounds for the nuclear norm of a tensor ⋮ Separability of Hermitian tensors and PSD decompositions ⋮ Further results for \(Z\)-eigenvalue localization theorem for higher-order tensors and their applications ⋮ Nonnegative forms with sublevel sets of minimal volume ⋮ On approximation algorithm for orthogonal low-rank tensor approximation ⋮ On norm compression inequalities for partitioned block tensors ⋮ On Tensors That Are Determined by Their Singular Tuples ⋮ Nonlinear Perron--Frobenius Theorems for Nonnegative Tensors ⋮ Rank properties and computational methods for orthogonal tensor decompositions ⋮ Extreme Ratio Between Spectral and Frobenius Norms of Nonnegative Tensors ⋮ Further results on tensor nuclear norms ⋮ Maximum relative distance between real rank-two and rank-one tensors ⋮ Symmetric Hermitian decomposability criterion, decomposition, and its applications ⋮ Hermitian Tensor Decompositions ⋮ Algebraic Methods for Tensor Data ⋮ Chebyshev Polynomials and Best Rank-one Approximation Ratio ⋮ On the tensor spectral \(p\)-norm and its dual norm via partitions

Uses Software

• Tensorlab

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