Skip to main content
SpringerLink
Log in

\(\mathrm{SOR}\)-Like Method for a New Generalized Absolute Value Equation

  • Research Articles
  • Published:
Mathematical Notes Aims and scope Submit manuscript

Abstract

In this paper, we extend the \(\mathrm{SOR}\)-like iteration method for a new generalized absolute value equation and obtain its convergence properties. What is more, the optimal parameter of the \(\mathrm{SOR}\)-like iteration is obtained. The result of numerical experiments shows that the proposed method is reliable and feasible.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1.
Fig. 2.
Fig. 3.

Similar content being viewed by others

References

  1. O. L. Mangasarian and R. R. Meyer, “Absolute value equations,” Linear Algebra Appl. 419 (2–3), 359–367 (2006).

    Article  MathSciNet  MATH  Google Scholar 

  2. S.-L. Wu and C.-X. Li, “The unique solution of the absolute value equations,” Appl. Math. Lett. 76, 195–200 (2018).

    Article  MathSciNet  MATH  Google Scholar 

  3. S.-L. Wu, “The unique solution of a class of the new generalized absolute value equation,” Appl. Math. Lett. 116, 107029 (2021).

    Article  MathSciNet  MATH  Google Scholar 

  4. O. L. Mangasarian, “A generalized Newton method for absolute value equations,” Optim. Lett. 3 (1), 101–108 (2009).

    Article  MathSciNet  MATH  Google Scholar 

  5. H.-Y. Zhou, S.-L. Wu, and C.-X. Li, “Newton-based matrix splitting method for generalized absolute value equation,” J. Comput. Appl. Math. 394, 113578 (2021).

    Article  MathSciNet  MATH  Google Scholar 

  6. M. Noor, J. Iqbal, and K. Noor, “On an iterative method for solving absolute value equations,” Optim. Lett. 6 (5), 1027–1033 (2012).

    Article  MathSciNet  MATH  Google Scholar 

  7. P. Guo, S.-L. Wu, and C.-X. Li, “On the \(\mathrm{SOR}\)-like iteration method for solving absolute value equations,” Appl. Math. Lett. 97, 107–113 (2019).

    Article  MathSciNet  Google Scholar 

  8. D. M. Young, Iterative Solution of Large Linear Systems (Academic Press, New York, 2014).

    Google Scholar 

  9. Y.-F. Ke, “The new iteration algorithm for absolute value equation,” Appl. Math. Lett. 99, 105990 (2020).

    Article  MathSciNet  MATH  Google Scholar 

Download references

Acknowledgments

The author wishes to express gratitude to the anonymous referees for their helpful comments.

Funding

This work was supported by the National Natural Science Foundation of China under grant no. 11961082.

Author information

Authors and Affiliations

  1. School of Mathematics, Yunnan Normal University, Kunming, 650500, PR China

    Shuan Yang & Shi-Liang Wu

Authors
  1. Shuan Yang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Shi-Liang Wu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Shuan Yang.

Additional information

Translated from Matematicheskie Zametki, 2023, Vol. 113, pp. 596–603 https://doi.org/10.4213/mzm13852.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Yang, S., Wu, SL. \(\mathrm{SOR}\)-Like Method for a New Generalized Absolute Value Equation. Math Notes 113, 567–573 (2023). https://doi.org/10.1134/S0001434623030276

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0001434623030276

Keywords

Search

Navigation