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

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 al...

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Bibliographic Details
Published inAIMS mathematics Vol. 6; no. 10; pp. 10846 - 10860
Main Authors Song, Xinnian, Gao, Lei
Format Journal Article
LanguageEnglish
Published AIMS Press 01.01.2021
Subjects
ckv-type b-matrices
error bounds
infinity norm
linear complementarity problems
p-matrices
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ISSN2473-6988
2473-6988
DOI10.3934/math.2021630

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Summary: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 $-matrices. It is proved that the new error bound is better than that provided by Li et al. [<xref ref-type="bibr" rid="b24">24 ] for DZ-type-$ B $-matrices, and than that provided by M. García-Esnaola and J.M. Peña [<xref ref-type="bibr" rid="b10">10 ] for $ B $-matrices in some cases. Numerical examples demonstrate the effectiveness of the obtained results.
ISSN:2473-6988
2473-6988
DOI:10.3934/math.2021630