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>

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 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 Relaxed Modulus-Based Matrix Splitting Methods for the Linear Complementarity Problem

Symmetry ◽  
2021 ◽  
Vol 13 (3) ◽  
pp. 503
Author(s):  
Shiliang Wu ◽  
Cuixia Li ◽  
Praveen Agarwal
Keyword(s):  
Fixed Point ◽  
Linear Complementarity Problem ◽  
Complementarity Problem ◽  
Sufficient Conditions ◽  
Linear Complementarity ◽  
Splitting Methods ◽  
Matrix Splitting ◽  
Numerical Examples ◽  
Iteration Methods ◽  
Point Form

In this paper, we obtain a new equivalent fixed-point form of the linear complementarity problem by introducing a relaxed matrix and establish a class of relaxed modulus-based matrix splitting iteration methods for solving the linear complementarity problem. Some sufficient conditions for guaranteeing the convergence of relaxed modulus-based matrix splitting iteration methods are presented. Numerical examples are offered to show the efficacy of the proposed methods.

A Convergent Algorithm for Generalized Linear Complementarity Problem in Engineering Modeling

2011 ◽  
Vol 267 ◽  
pp. 205-210
Author(s):  
Hong Chun Sun
Keyword(s):  
Error Bound ◽  
Linear Complementarity Problem ◽  
Complementarity Problem ◽  
Linear Complementarity ◽  
Generalized Linear Complementarity Problem ◽  
Levenberg Marquardt ◽  
Engineering Modeling ◽  
Convergent Algorithm

In this paper, we establish a error bound for the generalized linear complementtarity problem in engineering modeling(GLCP)which can be viewed as extensions of previously known results, based on which the famous Levenberg-Marquardt (L-M) algorithm is employed for obtaining its solution, and we show that the L-M algorithm is quadratically convergent without nondegenerate solution which is a new result for GLCP.

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