Skip to main content
SpringerLink
Log in

On Unbounded Tolerable Solution Sets

  • Published:
Reliable Computing

Abstract

We prove that the nonempty tolerable solution set of the interval linear system Ax = b is unbounded if and only if the interval matrix of the system has linearly dependent degenerate columns. Also, we prove that the tolerable solution set may be represented as a sum of the linear subspace {c ε ℝn ∨ Ac = 0} and a bounded convex polyhedron and propose a way for suitable estimation of unbounded tolerable solution sets.

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. Kearfott, R. B., Nakao, M. T., Neumaier, A., Rump, S. M., Shary, S. P., and van Hentenryck, P.: Standardized Notation in Interval Analysis, http://www.mat.univie.ac.at/~neum/software/int.

  2. Neumaier, A.: Interval Methods for Systems of Equations, Cambridge University Press, Cambridge, 1990.

    Google Scholar 

  3. Neumaier, A.: Tolerance Analysis with Interval Arithmetic, Freiburger Intervall-Berichte 86 (9), pp. 5–19.

  4. Rockafellar, R. T.: Convex Analysis, Prinston University Press, Prinston, New Jersey, 1970.

    Google Scholar 

  5. Rohn, J.: Inner Solutions of Linear Interval Systems, in: Nickel, K. (ed.), Interval Mathematics 1985, Lecture Notes in Computer Science 212, Springer-Verlag, New York, 1986, pp. 157–158.

  6. Shaidurov, V. V. and Shary, S. P.: Solution of Interval Algebraic Tolerance Problem, Preprint of Computer Center of Academy of Sciences No. 5, Krasnoyarsk, 1988 (in Russian).

  7. Shary, S. P.: A New Technique in Systems Analysis under Interval Uncertainty and Ambiguity, Reliable Computing 8 (5) (2002), pp. 321–419.

    Article  Google Scholar 

  8. Shary, S. P.: Solving the Linear Interval Tolerance Problem, Mathematics and Computers in Simulation 39 (1995), pp. 53–85, http://www.ict.nsc.ru/shary/Papers/LinTol.pdf.

Download references

Author information

Authors and Affiliations

  1. Institute of Computational Technologies, 6, Acad. Lavrentiev av., 630090, Novosibirsk, Russia

    Irene A. Sharaya

Authors
  1. Irene A. Sharaya
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Irene A. Sharaya.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Sharaya, I.A. On Unbounded Tolerable Solution Sets. Reliable Comput 11, 425–432 (2005). https://doi.org/10.1007/s11155-005-0049-9

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11155-005-0049-9

Keywords

Search

Navigation