A new error bound for linear complementarity problems involving $ B- $matrices

Hongmin Mo; Yingxue Dong; Hongmin Mo; Yingxue Dong

doi:10.3934/math.20231218

AIMS Mathematics

2023, Volume 8, Issue 10: 23889-23899. doi: 10.3934/math.20231218

Previous Article Next Article

Research article

A new error bound for linear complementarity problems involving $ B- $matrices

Hongmin Mo ^,,
Yingxue Dong

College of Mathematics and Statistics, Jishou University, Jishou 416000, China

Received: 20 October 2022 Revised: 20 February 2023 Accepted: 26 February 2023 Published: 07 August 2023
MSC : 65G50, 90C31, 90C33

In this paper, a new error bound for the linear complementarity problems of $ B- $matrices which is a subclass of the $ P- $matrices is presented. Theoretical analysis and numerical example illustrate that the new error bound improves some existing results.
- $ B- $matrices,
- linear complementarity problems,
- error bounds,
- diagonally dominant matrices
Citation: Hongmin Mo, Yingxue Dong. A new error bound for linear complementarity problems involving $ B- $matrices[J]. AIMS Mathematics, 2023, 8(10): 23889-23899. doi: 10.3934/math.20231218

Related Papers:

Abstract

In this paper, a new error bound for the linear complementarity problems of $ B- $matrices which is a subclass of the $ P- $matrices is presented. Theoretical analysis and numerical example illustrate that the new error bound improves some existing results.

References

[1]	X. J. Chen, S. H. Xiang, Perturbation bounds of P-matrix linear complementarity problems, SIAM J. Optim., 18 (2007), 1250–1265. https://doi.org/10.1137/060653019 doi: 10.1137/060653019
[2]	R. W. Cottle, J. S. Pang, R. E. Stone, The linear complementarity problem, Academic Press, San Diego, 1992.
[3]	K. G. Murty, Linear complementarity, linear and nonlinear programming, Heldermann Verlag, Berlin, 1998.
[4]	J. M. Peña, A class of P-matrices with applications to the localization of the eigenvalues of a real matrix, SIAM J. Matrix Anal. Appl., 22 (2001), 1027–1037. https://doi.org/10.1137/S0895479800370342 doi: 10.1137/S0895479800370342
[5]	X. Y. Chen, S. H. Xiang, Computation of error bounds for P-matrix linear complementarity problem, Math. Program., 106 (2006), 513–525. https://doi.org/10.1007/s10107-005-0645-9 doi: 10.1007/s10107-005-0645-9
[6]	P. N. Shivakumar, K. H. Chew, A sufficient condition for nonvanishing of determinants, Proc. Am. Math. Soc., 43 (1974), 63–66. https://doi.org/10.1002/pauz.19740030203 doi: 10.1002/pauz.19740030203
[7]	M. García-Esnaola, J. M. Peňa, Error bounds for linear complementarity problems for $B-$matrices, Appl. Math. Lett., 22 (2009), 1071–1075. https://doi.org/10.1016/j.aml.2008.09.001 doi: 10.1016/j.aml.2008.09.001
[8]	C. Q. Li, Y. T. Li, Note on error bounds for linear complementarity problems for $B-$matrices, Appl. Math. Lett., 57 (2016), 108–113. https://doi.org/10.1016/j.aml.2016.01.013 doi: 10.1016/j.aml.2016.01.013
[9]	C. Q. Li, Y. T. Li, Weakly chained diagonally dominant B-matrices and error bounds for linear complementarity problems, Numer. Algor., 73 (2016), 985–998. https://doi.org/10.1007/s11075-016-0125-8 doi: 10.1007/s11075-016-0125-8
[10]	R. Q. Zhao, A new upper bound of infinity norms of inverses for strictly diagonally dominant B-matrices, J. Sw. China. Normal. U., 45 (2020), 6–11.

Reader Comments

Your name:*

Email:*
© 2023 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)