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On the successive supersymmetric rank‐1 decomposition of higher‐order supersymmetric tensors
Author(s) -
Wang Yiju,
Qi Liqun
Publication year - 2007
Publication title -
numerical linear algebra with applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.02
H-Index - 53
eISSN - 1099-1506
pISSN - 1070-5325
DOI - 10.1002/nla.537
Subject(s) - mathematics , rank (graph theory) , tensor (intrinsic definition) , decomposition , diagonalizable matrix , order (exchange) , eigenvalues and eigenvectors , eigendecomposition of a matrix , combinatorics , pure mathematics , physics , symmetric matrix , quantum mechanics , chemistry , organic chemistry , finance , economics
In this paper, a successive supersymmetric rank‐1 decomposition of a real higher‐order supersymmetric tensor is considered. To obtain such a decomposition, we design a greedy method based on iteratively computing the best supersymmetric rank‐1 approximation of the residual tensors. We further show that a supersymmetric canonical decomposition could be obtained when the method is applied to an orthogonally diagonalizable supersymmetric tensor, and in particular, when the order is 2, this method generates the eigenvalue decomposition for symmetric matrices. Details of the algorithm designed and the numerical results are reported in this paper. Copyright © 2007 John Wiley & Sons, Ltd.