Skip to main content

A preconditioned general modulus-based matrix splitting iteration method for linear complementarity problems of H-matrices

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

Abstract

In this paper, we propose a preconditioned general modulus-based matrix splitting iteration method for solving modulus equations arising from linear complementarity problems. Its convergence theory is proved when the system matrix is an H+-matrix, from which some new convergence conditions can be derived for the (general) modulus-based matrix splitting iteration methods. Numerical results further show that the proposed methods are superior to the existing methods.

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

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

    Article  MathSciNet  Google Scholar 

  2. Bai, Z.-Z., Zhang, L.-L.: Modulus-based synchronous two-stage multisplitting iteration methods for linear complementarity problems. Numer. Algorithms 62, 59–77 (2013)

    Article  MathSciNet  Google Scholar 

  3. Berman, A., Plemmons, R.J.: Nonnegative Matrices in the Mathematical Sciences. SIAM Publisher, Philadelphia (1994)

    Book  Google Scholar 

  4. van Bokhoven, W.M.G.: Piecewise-Linear Modelling and Analysis. Proefschrift, Eindhoven (1981)

    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. Dong, J.L., Jiang, M.Q.: A modified modulus method for symmetric positive definite linear complementarity problems. Numerical Linear Algebra with Applications 16, 129–143 (2009)

    Article  MathSciNet  Google Scholar 

  7. Frommer, A., Mayer, G.: Convergence of relaxed parallel multisplitting methods. Linear Algebra Appl. 119, 141–152 (1989)

    Article  MathSciNet  Google Scholar 

  8. Li, W.: A general modulus-based matrix splitting method for linear complementarity problems of h- matrices. Appl. Math. Lett. 26, 1159–1164 (2013)

    Article  MathSciNet  Google Scholar 

  9. Li, W., Zheng, H.: A preconditioned modulus-based matrix splitting method for linear complementarity problems of h- matrices. Linear and Multilinear Algebra 64, 1390–1403 (2016)

    Article  MathSciNet  Google Scholar 

  10. Liu, S.-M., Zheng, H., Li, W.: A general accelerated modulus-based matrix splitting iteration method for solving linear complementarity problems. CALCOLO 53, 189–199 (2016)

    Article  MathSciNet  Google Scholar 

  11. Murty, K.G., Yu, F.T.: Linear Complementarity. Linear and Nonlinear Programming. Heldermann, Berlin (1988)

    MATH  Google Scholar 

  12. Zhang, L.-L.: Two-step modulus based matrix splitting iteration for linear complementarity problems. Numer. Algorithms 57, 83–99 (2011)

    Article  MathSciNet  Google Scholar 

  13. Zhang, L.-L., Ren, Z. -R.: Improved convergence theorems of modulus-based matrix splitting iteration methods for linear complementarity problems. Appl. Math. Lett. 26, 638–642 (2013)

    Article  MathSciNet  Google Scholar 

  14. Zheng, H., Li, W., Vong, S.-V.: A relaxation modulus-based matrix splitting iteration method for solving linear complementarity problems. Numer. Algorithms 74, 137–152 (2017)

    Article  MathSciNet  Google Scholar 

  15. Zheng, N., Yin, J.-F.: Accelerated modulus-based matrix splitting iteration methods for linear complementarity problems. Numer. Algorithms 64, 245–262 (2013)

    Article  MathSciNet  Google Scholar 

Download references

Funding

This work was partially supported by grants of National Natural Science Foundation of China (Nos. 11571124, 11671158 and 11771159) and China Postdoctoral Science Foundation (No. 2016M592505) and the doctoral start-up grant of Natural Science Foundation of Guangdong Province, China(2017A030310167).

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Xiaofei Peng.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Wu, X., Peng, X. & Li, W. A preconditioned general modulus-based matrix splitting iteration method for linear complementarity problems of H-matrices. Numer Algor 79, 1131–1146 (2018). https://doi.org/10.1007/s11075-018-0477-3

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11075-018-0477-3

Keywords