On approximate diagonalization of third order symmetric tensors by orthogonal transformations

被引：8

作者：

Li, Jianze ^{[1
]}

Usevich, Konstantin ^{[2
]}

Comon, Pierre ^{[1
]}

机构：

[1] Univ Grenoble Alpes, CNRS, Grenoble INP, GIPSA Lab, Grenoble, France

[2] Univ Lorraine, CNRS, CRAN, Nancy, France

来源：

LINEAR ALGEBRA AND ITS APPLICATIONS | 2019年 / 576卷

基金：

中国国家自然科学基金;

关键词：

Symmetric tensors; Orthogonally decomposable tensors; Approximate tensor diagonalization; Jacobi-type algorithms; Maximally diagonal tensors; DECOMPOSITION; RANK;

D O I：

10.1016/j.laa.2019.03.006

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we study the approximate orthogonal diagonalization problem of third order symmetric tensors. We define several classes of approximately diagonal tensors, including the ones corresponding to the stationary points of this problem. We study the relationships between these classes, and other well-known objects, such as tensor Z-eigenvalue and Z-eigenvector. We also prove results on convergence of the cyclic Jacobi (or Jacobi CoM2) algorithm. (C) 2019 Elsevier Inc. All rights reserved.

引用

页码：324 / 351

页数：28

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