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

Authors:
Guyan Ni;Yiju Wang
Affiliations:
Department of Mathematics, National University of Defense Technology, Changsha, Hunan, 410073, China;School of Management Sciences and Operations Research, Qufu Normal University, Rizhao Shandong, 276800, China and Department of Applied Mathematics, The Hong Kong Polytechnic University, Kowloon, ...
Venue:
Mathematical and Computer Modelling: An International Journal
Year:
2007

Citing 11
Cited 2

Apolarity and canonical forms for homogeneous polynomials

European Journal of Combinatorics - Special issue dedicated to Bernt Lindstro¨m
Independent component analysis, a new concept?

Signal Processing - Special issue on higher order statistics
Decomposition of quantics in sums of powers of linear forms

Signal Processing - Special issue on higher order statistics
High-order contrasts for independent component analysis

Neural Computation
A Multilinear Singular Value Decomposition

SIAM Journal on Matrix Analysis and Applications
On the Best Rank-1 and Rank-(R1,R2,. . .,RN) Approximation of Higher-Order Tensors

SIAM Journal on Matrix Analysis and Applications
Rank-One Approximation to High Order Tensors

SIAM Journal on Matrix Analysis and Applications
On the Best Rank-1 Approximation of Higher-Order Supersymmetric Tensors

SIAM Journal on Matrix Analysis and Applications
Tensor Rank and the Ill-Posedness of the Best Low-Rank Approximation Problem

SIAM Journal on Matrix Analysis and Applications
Symmetric Tensors and Symmetric Tensor Rank

SIAM Journal on Matrix Analysis and Applications
Eigenvalues of a real supersymmetric tensor

Journal of Symbolic Computation

Geometric entanglement of symmetric states and the majorana representation

TQC'10 Proceedings of the 5th conference on Theory of quantum computation, communication, and cryptography
Maximum Block Improvement and Polynomial Optimization

SIAM Journal on Optimization

Quantified Score

Hi-index	0.98

Visualization

Abstract

In this paper, we consider the best rank-1 approximation to higher-order symmetric tensors in the least-squares sense, and show that the best rank-1 approximation of a symmetric tensor with even order m can be determined by m/2 unit spheres and a best symmetric rank-1 approximation of a symmetric tensor with order 4 and dimension 2 is also its best rank-1 approximation.