A note on Banach's results concerning homogeneous polynomials associated with nonnegative tensors

DOI10.1007/s11590-020-01602-2zbMath1471.15005OpenAlexW3030543397WikidataQ114222160 ScholiaQ114222160MaRDI QIDQ828662

Chang Liang, Yuning Yang

Publication date: 5 May 2021

Published in: Optimization Letters (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11590-020-01602-2

zbMATH Keywords

tensoreigenvaluesingular valuePerron-Frobenius theoremmultivariate homogenous polynomial

Mathematics Subject Classification ID

Eigenvalues, singular values, and eigenvectors (15A18) Multilinear algebra, tensor calculus (15A69)

Cites Work

• On the reduction of multivariate quadratic systems to best rank-1 approximation of three-way tensors
• Some variational principles for \(Z\)-eigenvalues of nonnegative tensors
• Perron-Frobenius theorem for nonnegative tensors
• C-eigenvalue inclusion theorems for piezoelectric-type tensors
• Best rank one approximation of real symmetric tensors can be chosen symmetric
• Eigenvalues of a real supersymmetric tensor
• Quartic formulation of standard quadratic optimization problems
• Maximum Block Improvement and Polynomial Optimization
• On New Classes of Nonnegative Symmetric Tensors
• Further Results for Perron–Frobenius Theorem for Nonnegative Tensors
• On the successive supersymmetric rank-1 decomposition of higher-order supersymmetric tensors
• On the Best Rank-1 and Rank-(R₁ ,R₂ ,. . .,R_N) Approximation of Higher-Order Tensors
• Nuclear norm of higher-order tensors
• The Best Rank-1 Approximation of a Symmetric Tensor and Related Spherical Optimization Problems
• Norm attaining polynomials
• Tensor Analysis
• Most Tensor Problems Are NP-Hard

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