Skip to main content
Log in

Error bounds for linear complementarity problems of MB-matrices

  • Original Paper
  • Published:
Numerical Algorithms Aims and scope Submit manuscript

Abstract

In this paper, we present error bounds for the linear complementarity problem (LCP) with the system matrix being an MB-matrix based on its equivalent LCP, from which some error bounds for LCP with special system matrices are derived. The numerical results show the sharpness of the proposed bounds.

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

Access this article

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

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Ahn, B.-H.: Iterative methods for linear complementarity problems with upper-bounds on primary variables. Math. Program. 26, 295–315 (1983)

    Article  MATH  Google Scholar 

  2. Berman, A., Plemmons, R.-J.: Nonnegative Matrix in the Mathematical Sciences. SIAM Publisher, Philadelphia (1994)

    Book  Google Scholar 

  3. Bai, Z.-Z.: Modulus-based matrix splitting iteration methods for linear complementarity problems. Numer. Linear Algebra Appl. 17, 917–933 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  4. Chen, X.-J., Xiang, S.-H.: Computation of error bounds for P-matrix linear complementarity problems. Math. Program. Ser. A 106, 513–525 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  5. Cottle, R.-W., Pang, J.-S., Stone, R.-E.: The Linear Complementarity Problem. Academic Press, San Diego (1992)

    MATH  Google Scholar 

  6. Dai, P.-F.: Error bounds for linear complementarity problems of DB-matrices. Linear Algebra Appl. 434, 830–840 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  7. Dai, P.-F., Li, Y.-T., Lu, C.-J.: Error bounds for linear complementarity problems for SB-matrices. Numer. Algor. 61, 121–139 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  8. Dai, P.-F., Li, Y.-T., Lu, C.-J.: New error bounds for linear complementarity problem with an SB-matrices. Numer. Algor. 64, 741–757 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  9. Garcia-Esnaola, M., Peña, J.M.: Error bounds for linear complementarity problems for B-matrices. Appl. Math. Lett. 22, 1071–1075 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  10. Garcia-Esnaola, M., Peña, J.M.: Error bounds for linear complementarity problems involving B S-matrices. Appl. Math. Lett. 25, 1379–1383 (2012)

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  12. Garcia-Esnaola, M., Peña, J.M.: Error bounds for the linear complementarity problem with a Σ-SDD matrix. Linear Algebra Appl. 438, 1339–1346 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  13. Gao, Y.-M., Wang, X.-H.: Criteria for generalized diagonally dominant and M-matrices. Linear Algebra Appl. 268, 257–268 (1992)

    Article  Google Scholar 

  14. Horn, R.-A., Johnson, C.-R.: Matrix Analysis. Cambridge University Press, Cambridge (1985)

    Book  MATH  Google Scholar 

  15. Hu, J.-G.: Estimates of \(||B^{-1}A||_{\infty }\) and their applications. Math. Numer. Sin. 4 (3), 272–282 (1982)

    MATH  Google Scholar 

  16. Li, H.-B., Huang, T.-Z., Li, H.: On some subclasses of P-matrices. Numer. Linear Algebra Appl. 14, 391–405 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  17. Li, W., Zheng, H.: Some new error bounds for linear complementarity problems of H-matrices. Numer. Algor. 67(2), 257–269 (2014)

    Article  MATH  Google Scholar 

  18. Murty, K.-G.: Linear Complementarity, Linear and Nonlinear Programming. Heldermann Verlag, Berlin (1988)

    MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  20. Morac̆a, N.: Upper bounds for the infinity norm of the inverse of SDD and S-SDD matrices. J. Comput. Appl. Math. 206, 666–678 (2007)

    Article  MathSciNet  Google Scholar 

  21. Peña, J.-M.: On an alternative to Gershgorin circles and ovals of Cassini. Numer. Math. 95, 337–345 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  22. Sogabe, T.: Numerical algorithms for solving comrade linear systems based on tridiagonal solvers. Appl. Math. Comput. 198, 117–122 (2008)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Xianping Wu.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Chen, T., Li, W., Wu, X. et al. Error bounds for linear complementarity problems of MB-matrices. Numer Algor 70, 341–356 (2015). https://doi.org/10.1007/s11075-014-9950-9

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11075-014-9950-9

Keywords

Navigation