Partially doubly strictly diagonally dominant matrices with applications

Yi Liu; Lei Gao; Tianxu Zhao; Yi Liu; Lei Gao; Tianxu Zhao

doi:10.3934/era.2023151

Electronic Research Archive

2023, Volume 31, Issue 5: 2994-3013. doi: 10.3934/era.2023151

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Research article

Partially doubly strictly diagonally dominant matrices with applications

Yi Liu ¹,
Lei Gao ^{2
,
,},
Tianxu Zhao ²

1.
School of Mathematics and Computer Science, Yan'an University, Yan'an 716000, China
2.
School of Mathematics and Information Science, Baoji University of Arts and Sciences, Baoji 721013, China

Academic Editor: Xian-Ming Gu

Received: 28 November 2022 Revised: 02 March 2023 Accepted: 09 March 2023 Published: 20 March 2023

A new class of matrices called partially doubly strictly diagonally dominant (for shortly, PDSDD) matrices is introduced and proved to be a subclass of nonsingular $ H $-matrices, which generalizes doubly strictly diagonally dominant matrices. As applications, a new eigenvalue localization set for matrices is given, and an upper bound for the infinity norm bound of the inverse of PDSDD matrices is presented. Based on this bound, a new pseudospectra localization for matrices is derived and a lower bound for distance to instability is obtained.
- PDSDD matrices,
- eigenvalue localization,
- pseudospectra localization,
- infinity norm,
- $ H $-matrices
Citation: Yi Liu, Lei Gao, Tianxu Zhao. Partially doubly strictly diagonally dominant matrices with applications[J]. Electronic Research Archive, 2023, 31(5): 2994-3013. doi: 10.3934/era.2023151

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Abstract

A new class of matrices called partially doubly strictly diagonally dominant (for shortly, PDSDD) matrices is introduced and proved to be a subclass of nonsingular $ H $-matrices, which generalizes doubly strictly diagonally dominant matrices. As applications, a new eigenvalue localization set for matrices is given, and an upper bound for the infinity norm bound of the inverse of PDSDD matrices is presented. Based on this bound, a new pseudospectra localization for matrices is derived and a lower bound for distance to instability is obtained.

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