Robust eigenvectors of symmetric tensors - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue SIAM Journal on Matrix Analysis and Applications Année : 2022

Robust eigenvectors of symmetric tensors

Tommi Muller
  • Fonction : Auteur correspondant

Résumé

The tensor power method generalizes the matrix power method to higher-order arrays, or tensors. Like in the matrix case, the fixed points of the tensor power method are the eigenvectors of the tensor. While every real symmetric matrix has an eigendecomposition, the vectors generating a symmetric decomposition of a real symmetric tensor are not always eigenvectors of the tensor. In this paper we show that whenever an eigenvector is a generator of the symmetric decomposition of a symmetric tensor, then (if the order of the tensor is sufficiently high) this eigenvector is robust, i.e., it is an attracting fixed point of the tensor power method. We exhibit new classes of symmetric tensors whose symmetric decomposition consists of eigenvectors. Generalizing orthogonally decomposable tensors, we consider equiangular tight frame decomposable and equiangular set decomposable tensors. Our main result implies that such tensors can be decomposed using the tensor power method.

Dates et versions

hal-04312602 , version 1 (28-11-2023)

Identifiants

Citer

Tommi Muller, Elina Robeva, Konstantin Usevich. Robust eigenvectors of symmetric tensors. SIAM Journal on Matrix Analysis and Applications, 2022, 43 (4), pp.1784-1805. ⟨10.1137/21M1462052⟩. ⟨hal-04312602⟩
14 Consultations
0 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More