CKV-type $ B $-matrices and error bounds for linear complementarity problems

Xinnian Song; Lei Gao; Xinnian Song; Lei Gao

doi:10.3934/math.2021630

AIMS Mathematics

2021, Volume 6, Issue 10: 10846-10860. doi: 10.3934/math.2021630

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Research article

CKV-type $ B $-matrices and error bounds for linear complementarity problems

Xinnian Song ,
Lei Gao ^,

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

Received: 11 May 2021 Accepted: 16 July 2021 Published: 27 July 2021
MSC : 15A24, 15A60, 90C33, 65G50

In this paper, we introduce a new subclass of $ P $-matrices called Cvetković-Kostić-Varga type $ B $-matrices (CKV-type $ B $-matrices), which contains DZ-type-$ B $-matrices as a special case, and present an infinity norm bound for the inverse of CKV-type $ B $-matrices. Based on this bound, we also give an error bound for linear complementarity problems of CKV-type $ B $-matrices. It is proved that the new error bound is better than that provided by Li et al. ^[24] for DZ-type-$ B $-matrices, and than that provided by M. García-Esnaola and J.M. Peña ^[10] for $ B $-matrices in some cases. Numerical examples demonstrate the effectiveness of the obtained results.
- CKV-type $ B $-matrices,
- linear complementarity problems,
- error bounds,
- infinity norm,
- $ P $-matrices
Citation: Xinnian Song, Lei Gao. CKV-type $ B $-matrices and error bounds for linear complementarity problems[J]. AIMS Mathematics, 2021, 6(10): 10846-10860. doi: 10.3934/math.2021630

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Abstract

In this paper, we introduce a new subclass of $ P $-matrices called Cvetković-Kostić-Varga type $ B $-matrices (CKV-type $ B $-matrices), which contains DZ-type-$ B $-matrices as a special case, and present an infinity norm bound for the inverse of CKV-type $ B $-matrices. Based on this bound, we also give an error bound for linear complementarity problems of CKV-type $ B $-matrices. It is proved that the new error bound is better than that provided by Li et al. ^[24] for DZ-type-$ B $-matrices, and than that provided by M. García-Esnaola and J.M. Peña ^[10] for $ B $-matrices in some cases. Numerical examples demonstrate the effectiveness of the obtained results.

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