Error bounds for linear complementarity problems of strong $ SDD_{1} $ matrices and strong $ SDD_{1} $-$ B $ matrices

Yuanjie Geng; Deshu Sun; Yuanjie Geng; Deshu Sun

doi:10.3934/math.20231384

AIMS Mathematics

2023, Volume 8, Issue 11: 27052-27064. doi: 10.3934/math.20231384

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Research article

Error bounds for linear complementarity problems of strong $ SDD_{1} $ matrices and strong $ SDD_{1} $-$ B $ matrices

Yuanjie Geng ,
Deshu Sun ^,

College of Data Science and Information Engineering, Guizhou Minzu University, Guiyang 550025, China

Received: 17 August 2023 Revised: 09 September 2023 Accepted: 15 September 2023 Published: 22 September 2023
MSC : 15A48, 65G50, 90C31, 90C33

In this paper, an error bound for linear complementarity problems of strong $ SDD $$ _{1} $ matrices is given. By properties of $ SDD $$ _{1} $ matrices, a new subclass of $ P $-matrices called $ SDD_{1} $-$ B $ is presented, which contains $ B $-matrices. A new error bound of linear complementarity problems for $ SDD_{1} $-$ B $ is also provided, which improves the corresponding results. Numerical examples are given to illustrate the effectiveness of the obtained results.
- linear complementarity problems,
- error bound,
- strong $ SDD $$ _ {1} $ matrices,
- strong $ SDD $$ _ {1} $-$ B $ matrices,
- $ P $-matrices
Citation: Yuanjie Geng, Deshu Sun. Error bounds for linear complementarity problems of strong $ SDD_{1} $ matrices and strong $ SDD_{1} $-$ B $ matrices[J]. AIMS Mathematics, 2023, 8(11): 27052-27064. doi: 10.3934/math.20231384

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Abstract

In this paper, an error bound for linear complementarity problems of strong $ SDD $$ _{1} $ matrices is given. By properties of $ SDD $$ _{1} $ matrices, a new subclass of $ P $-matrices called $ SDD_{1} $-$ B $ is presented, which contains $ B $-matrices. A new error bound of linear complementarity problems for $ SDD_{1} $-$ B $ is also provided, which improves the corresponding results. Numerical examples are given to illustrate the effectiveness of the obtained results.

References

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