Some new results for $ B_1 $-matrices

Yan Li; Yaqiang Wang; Yan Li; Yaqiang Wang

doi:10.3934/era.2023244

Electronic Research Archive

2023, Volume 31, Issue 8: 4773-4787. doi: 10.3934/era.2023244

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Research article

Some new results for $ B_1 $-matrices

Yan Li ,
Yaqiang Wang ^,

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

Received: 29 March 2023 Revised: 03 June 2023 Accepted: 18 June 2023 Published: 07 July 2023

The class of $ B_1 $-matrices is a subclass of $ P $-matrices and introduced as a generalization of $ B $-matrices. In this paper, we present several properties for $ B_1 $-matrices. Then, the infinity norm upper bound for the inverse of $ B_1 $-matrices is obtained. Furthermore, the error bound for the linear complementarity problem of $ B_1 $-matrices is presented. Finally, some numerical examples are given to illustrate our results.
- $ B_1 $-matrices,
- $ SDD_1 $-matrices,
- $ P $-matrices,
- infinity norm,
- linear complementarity problem
Citation: Yan Li, Yaqiang Wang. Some new results for $ B_1 $-matrices[J]. Electronic Research Archive, 2023, 31(8): 4773-4787. doi: 10.3934/era.2023244

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Abstract

The class of $ B_1 $-matrices is a subclass of $ P $-matrices and introduced as a generalization of $ B $-matrices. In this paper, we present several properties for $ B_1 $-matrices. Then, the infinity norm upper bound for the inverse of $ B_1 $-matrices is obtained. Furthermore, the error bound for the linear complementarity problem of $ B_1 $-matrices is presented. Finally, some numerical examples are given to illustrate our results.

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