On the bound of the eigenvalue in module for a positive tensor
type: Item
instance of: scholarly article
title: On the bound of the eigenvalue in module for a positive tensor
zbMATH Open document ID: 1372.15014
author: Wen Li
author: Weihui Liu
author: Seak-Weng Vong
published in: Journal of the Operations Research Society of China
publication date: 2017-08-25T00:00:00Z
review text: The authors obtain a bound for a ratio of the largest eigenvalue and second largest eigenvalue in module for a higher-order tensor, following the definitions of eigenpairs introduced by \textit{L. Qi} [J. Symb. Comput. 40, No. 6, 1302--1324 (2005; Zbl 1125.15014)] and \textit{L. H. Lim} [``Singular values and eigenvalues of tensors: a variational approach'', in: Proceedings of the 1st IEEE international workshop on computational advances of multitensor adative processing. Piscataway, NJ: IEEE. 129--132 (2005; \url{doi:10.1109/CAMAP.2005.1574201})]. One can then deduce the bound of the second largest eigenvalue in module for a positive tensor, and the bound can reduce to the matrix cases. An inequality for \(H\)-eigenvalues is surmised.
Mathematics Subject Classification ID: 15A42
Mathematics Subject Classification ID: 15A69
zbMATH DE Number: 6764697
zbMATH Keywords: positive tensors
zbMATH Keywords: eigenvalue bound
reviewed by: Tin-Yau Tam
MaRDI profile type: Publication
full work available at URL: s40305-016-0142-2
OpenAlex ID: W2554788561
cites work: Finding the Largest Eigenvalue of a Nonnegative Tensor
cites work: Further Results for Perron–Frobenius Theorem for Nonnegative Tensors
cites work: Eigenvalues of a real supersymmetric tensor
cites work: A Multilinear Singular Value Decomposition
cites work: Perron-Frobenius theorem for nonnegative tensors
cites work: Perron-Frobenius theorem for nonnegative multilinear forms and extensions
cites work: Matrix theory
DOI: 10.1007/S40305-016-0142-2
description: scientific article; zbMATH DE number 6764697