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Research Article | Open Access

Generalized Perron complements in diagonally dominant matrices

Qin Zhong1( ), Na Li2( )
Department of Mathematics, Sichuan University Jinjiang College, Meishan 620860, China
School of Intelligence Technology, Geely University of China, Chengdu 641423, China
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Abstract

The concept of the generalized Perron complement concerning a nonnegative irreducible matrix was proposed by L. Z. Lu in 2002, and it was used to construct an algorithm for estimating the boundary of the spectral radius. In this study, we consider the properties of generalized Perron complements of nonnegative irreducible and diagonally dominant matrices. Moreover, we analyze the closure property of the generalized Perron complements of nonnegative irreducible H-matrices under certain conditions.

Keywords

irreducibilitynonnegative matrixdiagonally dominantgeneralized Perron complementH-matrix
CLC number: 15A18, 15A42, 15A48

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AIMS Mathematics
Volume 9 Issue 12,
December 2024
Pages 33879-33890
DOI: 10.3934/math.20241616

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Cite this article:
Zhong Q, Li N. Generalized Perron complements in diagonally dominant matrices. AIMS Mathematics, 2024, 9(12): 33879-33890. https://doi.org/10.3934/math.20241616

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Received: 20 September 2024
Revised: 10 November 2024
Accepted: 21 November 2024
Published: 15 December 2024
©2024 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)