Skip to main content
SpringerLink
Log in

Error bounds for linear complementarity problems of Nekrasov matrices

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

Abstract

We present error bounds for the linear complementarity problem when the involved matrix is a Nekrasov matrix and also when it is a \(\Sigma \)-Nekrasov matrix. The new bounds can improve considerably other previous bounds.

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.

Similar content being viewed by others

References

  1. Alanelli, M., Hadjidimos, A.: A new iterative criterion for H-matrices. SIAM J. Matrix Anal. Appl. 29, 160–176 (2006/07)

    Article  MathSciNet  Google Scholar 

  2. Berman, A., Plemmons, R.J.: Nonnegative matrices in the mathematical sciences. Classics in Applied Mathematics, vol. 9. SIAM, Philadelphia (1994)

  3. Bru, R., Giménez, I., Hadjidimos, A.: Is \(A \in C^{n\times n}\) a general H-matrix? Linear Algebra Appl. 436, 364–380 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  4. Chen, X., Xiang, S.: 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 Problems. Academic, Boston (1992)

    Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  7. Cvetković, L., Kostić, V., Doroslovaški, K.: Max-norm bounds for the inverse of S-Nekrasov matrices. Appl. Math. Comput. 218, 9498–9503 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  8. Cvetković, L., Dai, P.-F., Doroslovaški, K., Li, Y.T.: Infinity norm bounds for the inverse of Nekrasov matrices. Appl. Math. Comput. 219, 5020–5024 (2013)

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  11. Dai, P.F., Lu, C.J., Li, Y.T.: New error bounds for the linear complementarity problem with an SB-matrix. Numer. Algor., doi:10.1007/s11075-012-9691-6

  12. García-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 

  13. García-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 

  14. García-Esnaola, M., Peña, J.M.: Error bounds for linear complementarity problems of \(B^{S}\)-matrices. Appl. Math. Lett. 25, 1379–1383 (2012)

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  16. Li, B., Li, L., Harada, M., Niki, H., Tsatsomeros, M.J.: An iterative criterion for H-matrices. Linear Algebra Appl. 271, 179–190 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  17. 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 

  18. Szulc, T.: Some remarks on a theorem of Gudkov. Linear Algebra Appl. 225, 221–235 (1995)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Departamento de Matemática Aplicada, Universidad de Zaragoza, Zaragoza, Spain

    Marta García-Esnaola & Juan Manuel Peña

Authors
  1. Marta García-Esnaola
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Juan Manuel Peña
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Juan Manuel Peña.

Rights and permissions

Reprints and permissions

About this article

Cite this article

García-Esnaola, M., Peña, J.M. Error bounds for linear complementarity problems of Nekrasov matrices. Numer Algor 67, 655–667 (2014). https://doi.org/10.1007/s11075-013-9815-7

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11075-013-9815-7

Keywords

Mathematics Subject Classifications (2010)

Search

Navigation