Skip to main content
SpringerLink
Log in

Enclosing Solutions of Linear Complementarity Problems for H-Matrices

  • Published:
Reliable Computing

Abstract

The paper establishes a computational enclosure of the solution of the linear complementarity problem (q, M), where M is assumed to be an H-matrix with a positive main diagonal. A class of problems with interval data, which can arise in approximating the solutions of free boundary problems, is also treated successfully.

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

Similar content being viewed by others

References

  1. Alefeld, G., Chen, X., and Potra, F.: Validation of Solution to Linear Complementarity Problems, Numerische Mathematik 83 (1999), pp. 1–23.

    Google Scholar 

  2. Alefeld, G. and Herzberger, J.: Introduction to Interval Computations, Academic Press, New York and London, 1983.

    Google Scholar 

  3. Alefeld, G. and Shen, Z.: Miranda Theorem for Linear Complementarity Problems, Tech. Rept., 2003.

  4. Bierlein, J. C.: The Journal Bearing, Scientific American 233 (1975), pp. 50–64.

    Google Scholar 

  5. Cottle, R. W., Pang, J. S., and Stone, R. E.: Linear Complementarity Problem, Academic Press, Boston, 1992.

    Google Scholar 

  6. Cryer, C. W.: The Method of Christopherson for Solving Free Boundary Problems for Infinite Journal Bearings by Means of Finite Differences, Math. of Computation 25 (1971), pp. 435–443.

    Google Scholar 

  7. Miranda, C.: Un Osservazione su un teorema di Brouwer, Belletino Unione Math. Ital. Ser. 2(1940), pp. 3–7.

    Google Scholar 

  8. Moore, R. E.: A Test of Existence of Solutions to Nonlinear Systems, SIAM J. Numer. Anal. 14(1977), pp. 611–615.

    Google Scholar 

  9. Murty, K. G.: Linear Complementarity, Linear and Nonlinear Programming, Helderman, Berlin, 1988.

  10. Pang, J. S.: Newton's Method for B-Differentiable Equations, Mathematics of Operations Research 15 (1990), pp. 311–341.

    Google Scholar 

  11. Plemmons, R. J.: M-matrix Characterizations I: Nonsingular M-matrices, Linear Algebra and Its Applications 18 (1977), pp. 175–188.

    Google Scholar 

  12. Samelson, H., Thrall, R. M., and Wesler, O.: A Partition Theorem for Euclidean n-Space, Proceedings of the American Mathematical Society 9 (1958), pp. 805–807.

    Google Scholar 

  13. Schäfer, U.: An Enclosure Method for Free Boundary Problems Based on a Linear Complementarity Problem with Interval Data, Numer. Funct. Anal. Optim. 22 (2001), pp. 991–1011.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institut für Angewandte Mathematik, Universität, Karlsruhe, 76128, Karlsruhe, Germany, e-mail

    Götz Alefeld

  2. Department of Mathematics, Nanjing University, Nanjing, 210093, P.R.China, e-mail

    Zhengyu Wang & Zuhe Shen

Authors
  1. Götz Alefeld
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Zhengyu Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Zuhe Shen
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Alefeld, G., Wang, Z. & Shen, Z. Enclosing Solutions of Linear Complementarity Problems for H-Matrices. Reliable Computing 10, 423–435 (2004). https://doi.org/10.1023/B:REOM.0000047093.79994.8f

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/B:REOM.0000047093.79994.8f

Keywords

Search

Navigation