Some improved Ky Fan type eigenvalue inclusion sets for tensors
type: Item
instance of: scholarly article
title: Some improved Ky Fan type eigenvalue inclusion sets for tensors
zbMATH Open document ID: 1466.15008
author: Bing Zheng
author: Ruijuan Zhao
author: Yangyang Xu
published in: Calcolo
publication date: 2021-05-11T00:00:00Z
review text: Computing eigenvalues of a tensor is not easy when its order and dimension are large. One way to deal with the challenge is to find inclusion sets for the eigenvalues. Motivated by the work of \textit{K. Fan} [Duke Math. J. 25, 441--445 (1958; Zbl 0081.25202)] on eigenvalue inclusion set for matrices, \textit{Y. Yang} and \textit{Q. Yang} [SIAM J. Matrix Anal. Appl. 31, No. 5, 2517--2530 (2010; Zbl 1227.15014)] extended the Fan's result to tensors. \textit{J. He} and \textit{T.-Z. Huang} [J. Inequal. Appl. 2014, Paper No. 114, 9 p. (2014; Zbl 1372.15006)] obtained inclusion sets for the eigenvalues of a tensor via the theory of strong \(\mathcal M\)-tensors. This paper presents two classes of new Fan-type eigenvalue inclusion sets for tensors, which are tighter than those mentioned above. Under some conditions, the theoretical comparisons of the new proposed Fan-type eigenvalue inclusion sets are established and numerical examples are given.
Mathematics Subject Classification ID: 15A18
Mathematics Subject Classification ID: 15A69
Mathematics Subject Classification ID: 15A42
zbMATH DE Number: 7347037
zbMATH Keywords: Fan type
zbMATH Keywords: eigenvalue inclusion set
zbMATH Keywords: nonnegative tensor
zbMATH Keywords: \(\mathcal{Z}\)-tensor
Wikidata QID: Q114228543
reviewed by: Tin-Yau Tam
MaRDI profile type: Publication
full work available at URL: s10092-020-00389-z
OpenAlex ID: W3096383768
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DOI: 10.1007/S10092-020-00389-Z
description: scientific article; zbMATH DE number 7347037