Skip to main content
Log in

Enclosing solutions of linear interval equations is NP-hard

Die Lösungseinschließung bei linearen Intervall-Gleichungen ist NP-hart

  • Published:
Computing Aims and scope Submit manuscript

Abstract

We show that if the conjectureP≠NP is true, then there does not exist a general polynomial-time algorithm for enclosing the solution set of a system of linear interval equations.

Zusammenfassung

Unter Annahme der VermutungP≠NP wird gezeigt, daß es keinen allgemeinen polynomialen Algorithmus gibt, der die Intervallhülle der Lösungsmenge eines Systems linearer Intervall-Gleichungen einschließt.

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.

Similar content being viewed by others

References

  1. Alefeld, G., Herzberger, J.: Introduction to interval computations. New York: Academic Press 1983.

    Google Scholar 

  2. Garey, M. R., Johnson, D. S.: Computers and intractability: a guide to the theory of NP-completeness. San Francisco: Freeman 1979.

    Google Scholar 

  3. Neumaier, A.: Interval methods for systems of equations. Cambridge: Cambridge University Press 1990.

    Google Scholar 

  4. Poljak, S., Rohn, J.: Checking robust nonsingularity is NP-hard. Math. Control Signals Syst.6, 1–9 (1993).

    Article  MathSciNet  Google Scholar 

  5. Reichmann, K.: Abbruch beim Intervall-Gauss-Algorithmus. Computing,22, 355–361 (1979).

    Article  MATH  MathSciNet  Google Scholar 

  6. Rohn, J., Kreinovich, V.: Computing exact componentwise bounds on solutions, of linear systems with interval data is NP-hard (to appear in SIAM J. Matr. Anal.).

  7. Schrijver, A.: Theory of integer and linear programming. Chichester: Wiley 1986.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Rohn, J. Enclosing solutions of linear interval equations is NP-hard. Computing 53, 365–368 (1994). https://doi.org/10.1007/BF02307386

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02307386

AMS (MOS) Subject Classifications

Key words

Navigation