On the best rank-1 approximation to higher-order symmetric tensors

DOI10.1016/j.mcm.2007.01.008zbMath1149.65032OpenAlexW2020750014MaRDI QIDQ2472705

Guyan Ni, Y. J. Wang

Publication date: 22 February 2008

Published in: Mathematical and Computer Modelling (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.mcm.2007.01.008

zbMATH Keywords

invariantslinear elasticitysymmetric tensorsapproximation of higher-order tensorseven-order tensorsrank-1 tensors

Mathematics Subject Classification ID

Related Items (13)

Spherical optimization with complex variables for computing US-eigenpairs ⋮ SVD-Based Algorithms for the Best Rank-1 Approximation of a Symmetric Tensor ⋮ Global Rate Optimality of Integral Curve Estimators in High Order Tensor Models ⋮ The maximally entangled symmetric state in terms of the geometric measure ⋮ Iterative algorithms for computing US- and U-eigenpairs of complex tensors ⋮ Numerical multilinear algebra and its applications ⋮ CLASSIFICATION OF ENTANGLEMENT IN SYMMETRIC STATES ⋮ The geometric measure of entanglement for a symmetric pure state with non-negative amplitudes ⋮ Computing geometric measure of entanglement for symmetric pure states via the Jacobian SDP relaxation technique ⋮ Subtracting a best rank-1 approximation may increase tensor rank ⋮ Unfoldings and the rank-one approximation of the tensor ⋮ Matrix permanent and quantum entanglement of permutation invariant states ⋮ Estimation of integral curves from high angular resolution diffusion imaging (HARDI) data

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Eigenvalues and invariants of tensors
• Three-way arrays: rank and uniqueness of trilinear decompositions, with application to arithmetic complexity and statistics
• Apolarity and canonical forms for homogeneous polynomials
• Independent component analysis, a new concept?
• Decomposition of quantics in sums of powers of linear forms
• Eigenvalues of a real supersymmetric tensor
• Rank-One Approximation to High Order Tensors
• On the Best Rank-1 Approximation of Higher-Order Supersymmetric Tensors
• A Multilinear Singular Value Decomposition
• On the Best Rank-1 and Rank-(R₁ ,R₂ ,. . .,R_N) Approximation of Higher-Order Tensors
• Tensor Rank and the Ill-Posedness of the Best Low-Rank Approximation Problem
• Symmetric Tensors and Symmetric Tensor Rank

This page was built for publication: On the best rank-1 approximation to higher-order symmetric tensors