Programmable criteria for strong \(\mathcal {H}\)-tensors
type: Item
instance of: scholarly article
title: Programmable criteria for strong \(\mathcal {H}\)-tensors
zbMATH Open document ID: 1357.65048
author: Qilong Liu
author: Liqun Qi
author: Yaotang Li
published in: Numerical Algorithms
publication date: 2017-01-12T00:00:00Z
review text: A real tensor \(\mathcal A\) of order \(m\) and dimension \(n\) is called an \(\mathcal M\)-tensor if there exists a nonnegative tensor \(\mathcal B\) and a positive real number \(\eta \geq \rho({\mathcal B})\) such that \({\mathcal A}=\eta I - {\mathcal B}\). Here \(\rho(.)\) denotes the spectral radius. An \(\mathcal M\)-tensor \(\mathcal A=\eta I - {\mathcal B}\) is called a strong \(\mathcal M\)-tensor if \(\eta > \rho({\mathcal B})\). A tensor \(\mathcal A\) is called a strong \(\mathcal H\)-tensor if its comparison tensor is a strong \(\mathcal M\)-tensor. The definition of a comparison tensor is too complicated to be included here. However, since tensors generalize the notion of matrices, one could imagine a comparison tensor as an extension of a comparison matrix, quite well researched in the literature. The main contribution of the work reported, is in obtaining several sufficient conditions on the entries of a tensor \(\mathcal A\) which guarantee that \(\mathcal A\) is a strong \(\mathcal H\)-tensor. Consequently, an algorithm to identify strong \(\mathcal H\)-tensors is proposed. Numerical examples are used as illustrations.
reviewed by: Kanakadurga Sivakumar
Mathematics Subject Classification ID: 65F30
Mathematics Subject Classification ID: 15A72
zbMATH DE Number: 6674017
zbMATH Keywords: strong \(\mathcal {H}\)-tensors
zbMATH Keywords: positive semidefiniteness
zbMATH Keywords: irreducibility
zbMATH Keywords: strong \(\mathcal M\)-tensor
zbMATH Keywords: algorithm
zbMATH Keywords: numerical example
MaRDI profile type: Publication
full work available at URL: s11075-016-0145-4
OpenAlex ID: W2465974764
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DOI: 10.1007/S11075-016-0145-4
description: scientific article; zbMATH DE number 6674017