Generalized minimal Gershgorin set for tensors

Mohsen Tourang; Mostafa Zangiabadi; Chaoqian Li

doi:10.3934/jimo.2022106

Article Contents

2023, Volume 19, Issue 5: 3724-3741. Doi: 10.3934/jimo.2022106

This issue Previous Article A new feedback form of open-loop Stackelberg strategy in a general linear-quadratic differential game Next Article A unified and tight linear convergence analysis of the relaxed proximal point algorithm

Generalized minimal Gershgorin set for tensors

1.
Department of Mathematics, University of Hormozgan, P. O. Box 3995, Bandar Abbas, Iran
2.
School of Mathematics and Statistics, Yunnan University, Kunming 650091, China

^*Corresponding author: Mostafa Zangiabadi
^*Corresponding author: Mostafa Zangiabadi

Received: January 2022

Revised: March 2022

Early access: June 2022

Published: May 2023

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Abstract

Generalized minimal Gershgorin set is introduced to locate all generalized tensor eigenvalues. It is proved that this set is tighter than the well-known generalized Gershgorin set. A sequence of approximation sets were also conducted in order to obtain the generalized minimal Gershgorin set and prove that the limit of this sequence is the generalized minimal Gershgorin set. Furthermore, we use numerical examples and ﬁgures to illustrate the benefits of our results.

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Mathematics Subject Classification: Primary: 15A69, 15A18; Secondary: 65F15, 65F10, 15A42.

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Figure 1. $ \sigma (\mathcal{A},\mathcal{B}) \subseteq \Gamma^{\omega _4 } \left( {\mathcal{A},\mathcal{B}} \right) \subseteq \Gamma \left( {\mathcal{A},\mathcal{B}} \right) $

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Figure 2. $ \sigma (\mathcal{A},\mathcal{B}) \subseteq \Gamma^{\omega _4 } \left( {\mathcal{A},\mathcal{B}} \right) \subseteq \Gamma \left( {\mathcal{A},\mathcal{B}} \right) $

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