Infinity norm upper bounds for the inverse of $ SDD_1 $ matrices

Xiaoyong Chen; Yating Li; Liang Liu; Yaqiang Wang; Xiaoyong Chen; Yating Li; Liang Liu; Yaqiang Wang

doi:10.3934/math.2022493

AIMS Mathematics

2022, Volume 7, Issue 5: 8847-8860. doi: 10.3934/math.2022493

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Infinity norm upper bounds for the inverse of $ SDD_1 $ matrices

School of Mathematics and Information Science, Baoji University of Arts and Sciences, Baoji, Shaanxi, 721013, China

Received: 10 August 2021 Revised: 21 February 2022 Accepted: 25 February 2022 Published: 04 March 2022
MSC : 15A15, 15A48, 65F05, 65F40

In this paper, a new proof that $ SDD_1 $ matrices is a subclass of $ H $-matrices is presented, and some properties of $ SDD_1 $ matrices are obtained. Based on the new proof, some upper bounds of the infinity norm of inverse of $ SDD_1 $ matrices and $ SDD $ matrices are given. Moreover, we show that these new bounds of $ SDD $ matrices are better than the well-known Varah bound for $ SDD $ matrices in some cases. In addition, some numerical examples are given to illustrate the corresponding results.
- $ SDD_1 $ matrices,
- $ SDD $ matrices,
- upper bound,
- positive diagonal matrix,
- infinity norm
Citation: Xiaoyong Chen, Yating Li, Liang Liu, Yaqiang Wang. Infinity norm upper bounds for the inverse of $ SDD_1 $ matrices[J]. AIMS Mathematics, 2022, 7(5): 8847-8860. doi: 10.3934/math.2022493

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Abstract

In this paper, a new proof that $ SDD_1 $ matrices is a subclass of $ H $-matrices is presented, and some properties of $ SDD_1 $ matrices are obtained. Based on the new proof, some upper bounds of the infinity norm of inverse of $ SDD_1 $ matrices and $ SDD $ matrices are given. Moreover, we show that these new bounds of $ SDD $ matrices are better than the well-known Varah bound for $ SDD $ matrices in some cases. In addition, some numerical examples are given to illustrate the corresponding results.

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