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Global error bounds for the extended vertical LCP of B-type matrices

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Abstract

Some computable global error bounds for the extended vertical linear complementarity problem of B-type matrices are given. The new error bounds are sharper than those presented in Zhang et al. (Comput Optim Appl 42(3):335–352, 2009) on some concrete examples.

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References

  • Berman A, Plemmons R (1994) Nonnegative matrices in the mathematical sciences. SIAM, Philadelphia

    Book  Google Scholar 

  • Chen XJ, Xiang SH (2006) Computation of error bounds for \(P\)-matrix linear complementarity problems. Math Progr 106(3):513–525

    Article  MathSciNet  Google Scholar 

  • Cottle RW, Dantzig GB (1970) A generalization of the linear complementarity problem. J Comb Theory Ser A 8(1):79–90

    Article  MathSciNet  Google Scholar 

  • Dai PF (2011) Error bounds for linear complementarity problems of \(DB\)-matrices. Linear Algebra Appl 434:830–840

    Article  MathSciNet  Google Scholar 

  • García-Esnaola M, Peña JM (2009) Error bounds for linear complementarity problems for \(B\)-matrices. Appl Math Lett 22(7):1071–1075

    Article  MathSciNet  Google Scholar 

  • García-Esnaola M, Peña JM (2017) \(B_\pi ^R\)-matrices and error bounds for linear complementarity problems. Calcolo 54(3):813–822

    Article  MathSciNet  Google Scholar 

  • Genot F, Brogliato B, Brach RM et al (1997) On LCPs and tangential impacts in rigid body mechanics with unilateral constraints and dry friction. IFAC Proc Vol 30(20):809–816

    Article  Google Scholar 

  • Gowda MS, Sznajder R (1994) The generalized order linear complementarity problem. SIAM J Matrix Anal Appl 15(3):779–795

    Article  MathSciNet  Google Scholar 

  • Hou ZW, Jing X, Gao L (2019) New error bounds for linear complementarity problems of \(\Sigma \)-SDD matrices and \(SB\)-matrices. Open Math 17(1):1599–1614

    Article  MathSciNet  Google Scholar 

  • Li CQ, Cvetković Lj, Wei YM, Zhao JX (2019) An infinity norm bound for the inverse of Dashnic–Zusmanovich type matrices with applications. Linear Algebra Appl 565:99-122

  • Li CQ, Yang SR, Huang H, Li YT, Wei YM (2020) Note on error bounds for linear complementarity problems of Nekrasov matrices. Numer Algorithms 83:355–372

    Article  MathSciNet  Google Scholar 

  • Mendes-Arajo C, Mendes-Gonalves S (2019) On a class of nonsingular matrices containing \(B\)-matrices. Linear Algebra Appl 578:356–369

    Article  MathSciNet  Google Scholar 

  • Mathias R, Pang JS (1990) Error bounds for the linear complementarity problem with a \(P\)-matrix. Lznear Algebra Appl 132:123–136

    Article  MathSciNet  Google Scholar 

  • Neumann M, Peña JM, Pryporova O (2013) Some classes of nonsingular matrices and applications. Linear Algebra Appl 438(4):1936–1945

    Article  MathSciNet  Google Scholar 

  • Peña JM (2000) A class of \(P\)-Matrices with applications to the localization of the eigenvalues of a real matrix. SIAM J Matrix Anal Appl 22(4):1027–1037

    Article  MathSciNet  Google Scholar 

  • Peña JM (2003) On an alternative to Gerschgorin circles and ovals of Cassini. Numer Math 95(2):337–345

    Article  MathSciNet  Google Scholar 

  • Sang CL, Chen Z (2019) A new error bound for linear complementarity problems of weakly chained diagonally dominant \(B\)-matrices. Linear Multilinear Algebra. https://doi.org/10.1080/03081087.2019.1649995

  • Stavroulakis GE (1999) Impact-echo from a unilateral interlayer crack. LCPCBEM modelling and neural identification. Eng Fract Mech 62(2):165–184

  • Sznajder R, Gowda MS (1995) Generalizations of \(P_0\)-and \(P\)-properties; extended vertical and horizontal linear complementarity problems. Linear Algebra Appl 223–224:695–715

    Article  Google Scholar 

  • Varah JM (1975) A lower bound for the smallest singular value of a matrix. Linear Algebra Appl 11:3–5

    Article  MathSciNet  Google Scholar 

  • Xiu NH, Zhang JZ (2002) A characteristic quantity of \(P\)-matrices. Appl Math Lett 15:41–46

    Article  MathSciNet  Google Scholar 

  • Yong L (2011) Linear complementarity problem and multiobjective optimization. Appl Mech Mater 101–102:236–239

    Article  Google Scholar 

  • Zhang C, Chen XJ, Xiu N (2009) Global error bounds for the extended vertical LCP. Comput Optim Appl 42(3):335–352

    Article  MathSciNet  Google Scholar 

Download references

Acknowledgements

The authors are grateful to the anonymous referees for their constructive comments and suggestions, which greatly improve our manuscript. This work is supported in part by the National Natural Science Foundation of China (No. 12061087), the Applied Basic Research Programs of Science and Technology Department of Yunnan Province (No. 2018FB001), Program for Excellent Young Talents, Yunnan University, and Yunnan Provincial Ten Thousands Plan Young Top Talents.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Yunnan University, Yunnan, 650091, China

    Hehui Wang & Chaoqian Li

  2. Jilin Vocational college of Industry and Technology, Jilin, 132013, China

    Haibin Zhang

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  1. Hehui Wang
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  2. Haibin Zhang
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  3. Chaoqian Li
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Correspondence to Chaoqian Li.

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Communicated by Yimin Wei.

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Wang, H., Zhang, H. & Li, C. Global error bounds for the extended vertical LCP of B-type matrices. Comp. Appl. Math. 40, 148 (2021). https://doi.org/10.1007/s40314-021-01528-0

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