scholarly journals New error bounds for linear complementarity problems of Σ-SDD matrices and SB-matrices

2019 ◽  
Vol 17 (1) ◽  
pp. 1599-1614
Author(s):  
Zhiwu Hou ◽  
Xia Jing ◽  
Lei Gao
Keyword(s):  
Linear Algebra ◽  
Error Bound ◽  
Linear Complementarity Problem ◽  
Error Bounds ◽  
Complementarity Problems ◽  
Linear Complementarity Problems ◽  
Linear Complementarity ◽  
Numerical Examples ◽  
Numer Algor ◽  
Better Than

Abstract A new error bound for the linear complementarity problem (LCP) of Σ-SDD matrices is given, which depends only on the entries of the involved matrices. Numerical examples are given to show that the new bound is better than that provided by García-Esnaola and Peña [Linear Algebra Appl., 2013, 438, 1339–1446] in some cases. Based on the obtained results, we also give an error bound for the LCP of SB-matrices. It is proved that the new bound is sharper than that provided by Dai et al. [Numer. Algor., 2012, 61, 121–139] under certain assumptions.

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

2021 ◽  
Vol 6 (10) ◽  
pp. 10846-10860
Author(s):  
Xinnian Song ◽  
◽  
Lei Gao
Keyword(s):  
Error Bound ◽  
Complementarity Problems ◽  
Linear Complementarity Problems ◽  
Linear Complementarity ◽  
Type B ◽  
Numerical Examples ◽  
Infinity Norm ◽  
Norm Bound ◽  
Special Case ◽  
Better Than

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

scholarly journals A new error bound for linear complementarity problems for B-matrices

2016 ◽  
Vol 31 ◽  
pp. 476-484 ◽  
Author(s):  
Chaoqian Li ◽  
Mengting Gan ◽  
Shaorong Yang
Keyword(s):  
Error Bound ◽  
Linear Complementarity Problem ◽  
Error Bounds ◽  
Complementarity Problem ◽  
Complementarity Problems ◽  
Linear Complementarity Problems ◽  
Linear Complementarity ◽  
Appl Math

A new error bound for the linear complementarity problem is given when the involved matrix is a $B$-matrix. It is shown that this bound improves the corresponding result in [M. Garc\'{i}a-Esnaola and J.M. Pe\~{n}a. Error bounds for linear complementarity problems for $B$-matrices. {\em Appl. Math. Lett.}, 22:1071--1075, 2009.] in some cases, and that it is sharper than that in [C.Q. Li and Y.T. Li. Note on error bounds for linear complementarity problems for $B$-matrices. {\em Appl. Math. Lett.}, 57:108--113, 2016.].

scholarly journals Norm bounds for the inverse and error bounds for linear complementarity problems for {P1,P2}-Nekrasov matrices

Filomat ◽  
2021 ◽  
Vol 35 (1) ◽  
pp. 239-250
Author(s):  
M. Nedovic ◽  
Lj. Cvetkovic
Keyword(s):  
Error Bound ◽  
Error Bounds ◽  
Complementarity Problems ◽  
Linear Complementarity Problems ◽  
Linear Complementarity ◽  
Numerical Examples ◽  
Different Types ◽  
Nekrasov Matrices

{P1,P2}-Nekrasov matrices represent a generalization of Nekrasov matrices via permutations. In this paper, we obtained an error bound for linear complementarity problems for fP1; P2g-Nekrasov matrices. Numerical examples are given to illustrate that new error bound can give tighter results compared to already known bounds when applied to Nekrasov matrices. Also, we presented new max-norm bounds for the inverse of {P1,P2}-Nekrasov matrices in the block case, considering two different types of block generalizations. Numerical examples show that new norm bounds for the block case can give tighter results compared to already known bounds for the point-wise case.

scholarly journals The Solution Set Characterization and Error Bound for the Extended Mixed Linear Complementarity Problem

2012 ◽  
Vol 2012 ◽  
pp. 1-15
Author(s):  
Hongchun Sun ◽  
Yiju Wang
Keyword(s):  
Error Bound ◽  
Linear Complementarity Problem ◽  
Complementarity Problem ◽  
Complementarity Problems ◽  
Linear Complementarity Problems ◽  
Linear Complementarity ◽  
Solution Set ◽  
Global Error Bound ◽  
Mixed Linear Complementarity Problem

For the extended mixed linear complementarity problem (EML CP), we first present the characterization of the solution set for the EMLCP. Based on this, its global error bound is also established under milder conditions. The results obtained in this paper can be taken as an extension for the classical linear complementarity problems.

scholarly journals New error bounds for linear complementarity problems of weakly chained diagonally dominant B-matrices

2017 ◽  
Vol 15 (1) ◽  
pp. 978-986 ◽  
Author(s):  
Deshu Sun ◽  
Feng Wang
Keyword(s):  
Error Bounds ◽  
Complementarity Problems ◽  
Linear Complementarity Problems ◽  
Linear Complementarity ◽  
Numerical Examples ◽  
Diagonally Dominant

Abstract Some new error bounds for the linear complementarity problems are obtained when the involved matrices are weakly chained diagonally dominant B-matrices. Numerical examples are given to show the effectiveness of the proposed bounds.

scholarly journals New error bound for linear complementarity problem of $ S $-$ SDDS $-$ B $ matrices

2022 ◽  
Vol 7 (2) ◽  
pp. 3239-3249
Author(s):  
Lanlan Liu ◽  
◽  
Pan Han ◽  
Feng Wang
Keyword(s):  
Error Bound ◽  
Linear Complementarity Problem ◽  
Complementarity Problem ◽  
Linear Complementarity ◽  
Numerical Examples

<abstract><p>$ S $-$ SDDS $-$ B $ matrices is a subclass of $ P $-matrices which contains $ B $-matrices. New error bound of the linear complementarity problem for $ S $-$ SDDS $-$ B $ matrices is presented, which improves the corresponding result in <sup>[<xref ref-type="bibr" rid="b1">1</xref>]</sup>. Numerical examples are given to verify the corresponding results.</p></abstract>

Note on error bounds for linear complementarity problems of Nekrasov matrices

2019 ◽  
Vol 83 (1) ◽  
pp. 355-372 ◽  
Author(s):  
Chaoqian Li ◽  
Shaorong Yang ◽  
Hui Huang ◽  
Yaotang Li ◽  
Yimin Wei
Keyword(s):  
Error Bounds ◽  
Complementarity Problems ◽  
Linear Complementarity Problems ◽  
Linear Complementarity ◽  
Nekrasov Matrices
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