Bounds on the Spectral Norm and the Nuclear Norm of a Tensor Based on Tensor Partitions

DOI10.1137/15M1028777zbMath1348.15018OpenAlexW2528781329MaRDI QIDQ2827070

Zhening Li

Publication date: 12 October 2016

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

Full work available at URL: https://doi.org/10.1137/15m1028777

zbMATH Keywords

spectral normnuclear normapproximation boundtensor normblock tensortensor partition

Mathematics Subject Classification ID

Approximation methods and heuristics in mathematical programming (90C59) Norms of matrices, numerical range, applications of functional analysis to matrix theory (15A60) Computational difficulty of problems (lower bounds, completeness, difficulty of approximation, etc.) (68Q17) Multilinear algebra, tensor calculus (15A69)

Related Items (11)

Combinatorial methods for the spectral \(p\)-norm of hypermatrices ⋮ On norm compression inequalities for partitioned block tensors ⋮ Extreme Ratio Between Spectral and Frobenius Norms of Nonnegative Tensors ⋮ Further results on tensor nuclear norms ⋮ Approximating Tensor Norms via Sphere Covering: Bridging the Gap between Primal and Dual ⋮ Synthetic Aperture Imaging and Motion Estimation Using Tensor Methods ⋮ Algebraic Methods for Tensor Data ⋮ A concise proof to the spectral and nuclear norm bounds through tensor partitions ⋮ On the tensor spectral \(p\)-norm and its dual norm via partitions ⋮ Perturbation theory for Moore-Penrose inverse of tensor via Einstein product ⋮ Spectral norm and nuclear norm of a third order tensor

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