scholarly journals Note on error bounds for linear complementarity problems involving $ B^S $-matrices

2021 ◽  
Vol 7 (2) ◽  
pp. 1896-1906
Author(s):  
Deshu Sun ◽  
Keyword(s):  
Error Bounds ◽  
Complementarity Problems ◽  
Matrix Theory ◽  
Linear Complementarity Problems ◽  
Linear Complementarity ◽  
Upper Bounds ◽  
Theory Analysis ◽  
Infinity Norm ◽  
S Matrix ◽  
Diagonally Dominant

<abstract><p>Using the range for the infinity norm of inverse matrix of a strictly diagonally dominant $ M $-matrix, some new error bounds for the linear complementarity problem are obtained when the involved matrix is a $ B^S $-matrix. Theory analysis and numerical examples show that these upper bounds are more accurate than some existing results.</p></abstract>

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 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.

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

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>

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