Generalized Perron complements in diagonally dominant matrices

Qin Zhong; Na Li; Qin Zhong; Na Li

doi:10.3934/math.20241616

AIMS Mathematics

2024, Volume 9, Issue 12: 33879-33890. doi: 10.3934/math.20241616

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Research article

Generalized Perron complements in diagonally dominant matrices

Qin Zhong ^{1
,
,},
Na Li ^{2
,
,}

1.
Department of Mathematics, Sichuan University Jinjiang College, Meishan 620860, China
2.
School of Intelligence Technology, Geely University of China, Chengdu 641423, China

Received: 20 September 2024 Revised: 10 November 2024 Accepted: 21 November 2024 Published: 29 November 2024
MSC : 15A18, 15A42, 15A48

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.
- irreducibility,
- nonnegative matrix,
- diagonally dominant,
- generalized Perron complement,
- $ H $-matrix
Citation: Qin Zhong, Na Li. Generalized Perron complements in diagonally dominant matrices[J]. AIMS Mathematics, 2024, 9(12): 33879-33890. doi: 10.3934/math.20241616

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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.

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