Skip to main content
Log in

New error bounds for linear complementarity problems of S-Nekrasov matrices and BS-Nekrasov matrices

  • Published:
Computational and Applied Mathematics Aims and scope Submit manuscript

Abstract

In this paper, we give new error bounds for linear complementarity problems when the involved matrices are S-Nekrasov matrices and BS-Nekrasov matrices, respectively. We prove that the obtained bounds are better than those of Gao et al. (J Comput Appl Math 336:147–159, 2018) in some cases.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  • Berman A, Plemmons RJ (1979) Nonnegative matrix in the mathematical sciences. Academic Press, New York

    MATH  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  • Chen XJ, Xiang SH (2007) Perturbation bounds of \(P\)-matrix linear complementarity problems. SIAM J Optim 18:1250–1265

    Article  MathSciNet  Google Scholar 

  • Chen TT, Li W, Wu X, Vong S (2015) Error bounds for linear complementarity problems of \(MB\)-matrices. Numer Algorithms 70(2):341–356

    Article  MathSciNet  Google Scholar 

  • Cottle RW, Pang JS, Stone RE (1992) The linear complementarity problem. Academic Press, San Diego

    MATH  Google Scholar 

  • Cvetković L, Kostić V, Rauški S (2009) A new subclass of \(H\)-matrices. Appl Math Comput 208:206–210

    MathSciNet  MATH  Google Scholar 

  • Dafermos S (1980) Traffic equilibrium and variational inequalities. Transp Sci 14:42–54

    Article  MathSciNet  Google Scholar 

  • Dai PF, Li JC, Bai JC, Dong LQ (2018) Notes on new error bounds for the linear complementarity problem of Nekrasov matrices, \(B\)-Nekrasov matrices and \(QN\)-matrices. Numer Math Theor Meth Appl (accepted)

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

    Article  MathSciNet  Google Scholar 

  • Dai PF, Li YT, Lu CJ (2012) Error bounds for linear complementarity problems for \(SB\)-matrices. Numer Algorithms 61:121–139

    Article  MathSciNet  Google Scholar 

  • Dai PF, Lu CJ, Li YT (2013) New error bounds for the linear complementarity problem with an \(SB\)-matrix. Numer Algorithms 64:741–757

    Article  MathSciNet  Google Scholar 

  • Dai PF, Li JC, Li YT, Zhang CY (2016) Error bounds for the linear complementarity problem of \(QN\)-matrices. Calcolo 53:647–657

    Article  MathSciNet  Google Scholar 

  • Dai PF, Li JC, Li YT, Bai JC (2017) A general preconditioner for linear complementarity problem with an \(M\)-matrix. J Comput Appl Math 317:100–112

    Article  MathSciNet  Google Scholar 

  • Ferris MC, Pang JS (1997) Engineering and economic applications of complementarity problems. SIAM Rev 39:669–713

    Article  MathSciNet  Google Scholar 

  • Gao L, Li CQ, Li YT (2018) An improvement of the error bounds for linear complementarity problems of Nekrasov matrices. Linear Multilinear Algebra 66(8):1505–1519

    Article  MathSciNet  Google Scholar 

  • Gao L, Wang YQ, Li CQ (2018) New error bounds for the linear complementarity problem of QN-matrices. Numer Algorithms 77:229–242

    Article  MathSciNet  Google Scholar 

  • Gao L, Wang YQ, Li CQ, Li YT (2018) Error bounds for the linear complementarity problem of \(S\)-Nekrasov matrices and \(B\)-\(S\)-Nekrasov matrices. J Comput Appl Math 336:147–159

    Article  MathSciNet  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  • García-Esnaola M, Peña JM (2010) A comparison of error bounds for linear complementarity problems of \(H\)-matrices. Linear Algebra Appl 433:956–964

    Article  MathSciNet  Google Scholar 

  • García-Esnaola M, Peña JM (2014) Error bounds for linear complementarity problems of Nekrasov matrices. Numer Algorithms 67:655–667

    Article  MathSciNet  Google Scholar 

  • García-Esnaola M, Peña JM (2016) \(B\)-Nekrasov matrices and error bounds for linear complementarity problems. Numer Algorithms 72(2):435–445

    Article  MathSciNet  Google Scholar 

  • Kolotilina LY (2015) Bounds for the inverses of generalized Nekrasov matrices. J Math Sci 207:786–794

    Article  MathSciNet  Google Scholar 

  • Li CQ, Li YT (2016a) Note on error bounds for linear complementarity problems for \(B\)-matrices. Appl Math Lett 57:108–113

  • Li CQ, Li YT (2016b) Weakly chained diagonally dominant \(B\)-matrices and error bounds for linear complementarity problems. Numer Algorithms 73:985–998

    Article  MathSciNet  Google Scholar 

  • Li CQ, Gan M, Yang S (2016) A new error bounds for linear complementarity problems for \(B\)-matrices. Electron J Linear Algebra 31:476–484

    Article  MathSciNet  Google Scholar 

  • Li CQ, Dai PF, Li YT (2017) New error bounds for linear complementarity problems of Nekrasov matrices and \(B\)-Nekrasov matrices. Numer Algorithms 74:997–1009

    Article  MathSciNet  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  • Schäer U (2004) A linear complementarity problem with a \(P\)-matrix. SIAM Rev 46:189–201

    Article  MathSciNet  Google Scholar 

  • Schäfer U (2001) An enclosure method for free boundary problems based on a linear complementarity problem with interval data. Numer Funct Anal Optim 22:991–1011

    Article  MathSciNet  Google Scholar 

  • Sun D, Wang F (2018) New error bound for linear complementarity problems for \(B\)-matrices. Linear Multilinear Algebra 66(11):2156–2167

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Ping-Fan Dai.

Additional information

Communicated by Jinyun Yuan.

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

This work is partly supported by the National Natural Science Foundation of China (11671318), the Natural Science Foundation of Fujian province (2016J01028).

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Dai, PF., Li, J., Bai, J. et al. New error bounds for linear complementarity problems of S-Nekrasov matrices and BS-Nekrasov matrices. Comp. Appl. Math. 38, 61 (2019). https://doi.org/10.1007/s40314-019-0818-4

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s40314-019-0818-4

Keywords

Mathematics Subject Classification

Navigation

pFad - Phonifier reborn

Pfad - The Proxy pFad of © 2024 Garber Painting. All rights reserved.

Note: This service is not intended for secure transactions such as banking, social media, email, or purchasing. Use at your own risk. We assume no liability whatsoever for broken pages.


Alternative Proxies:

Alternative Proxy

pFad Proxy

pFad v3 Proxy

pFad v4 Proxy