Skip to main content
SpringerLink
Log in

Interval and Twin Arithmetics

  • Published:
Reliable Computing

Abstract

The problem of finding inner and outer estimations of the range of values of a real function is considered. An overview of interval arithmetics being used for improvement of outer estimations is given. The twin arithmetic is introduced for simultaneous inner and outer estimations and directed twin arithmetic is proposed as generalization of the directed interval arithmetic.

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. Gardeñes, E. and Trepat, A.: The Interval Computing System SIGLA-PL/1(0), Freiburger Intervall-Berichte 8 (1979).

  2. Gardeñes, E. and Trepat, A.: Fundamentals of SIGLA, an Interval Computing System over the Completed Set of Intervals, Computing 24 (1980), pp. 161–179.

    Google Scholar 

  3. Gardeñes, E., Trepat, A., and Janer, J. M.: SIGLA-PL/1 Development and Applications, in: Nickel, K. (ed.), Interval Mathematics. Academic Press, N.Y., 1980, pp. 301–315

    Google Scholar 

  4. Kaucher, E.: Interval Analysis in the Extended Interval Space IR, Computing Supplementum 2 (1980), pp. 33–49.

    Google Scholar 

  5. Kreinovich, V., Nesterov, V. M., and Zheludeva, N. A.: Interval Methods That Are Guaranteed to Underestimate (and the Resulting New Justification of Kaucher Arithmetic), Reliable Computing 2(2) (1996), pp. 119–124.

    Google Scholar 

  6. Markov, S. M.: On the Presentation of Ranges of Monotone Functions Using Interval Arithmetic, Interval Computations 4(6) (1992), pp. 19–31.

    Google Scholar 

  7. Markov, S. M.: Extended Interval Arithmetic Involving Infinite Intervals, Mathematica Balkanica 6 (1992), pp. 269–304.

    Google Scholar 

  8. Markov, S. M.: On Directed Interval Arithmetic and Its Applications, J. UCS 2(7) (1995), pp. 510–521.

    Google Scholar 

  9. Nesterov, V. M.: How to Use Monotonicity-Type Information to Get Better Estimates of the Range of Real-Valued Functions, Interval Computations 4 (1993), pp. 3–12

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. St. Petersburg Institute for Informatics and Automation, Russian Academy of Sciences, 14-th line, 39, V.O., 199178, St. Petersburg, Russia

    Vyacheslav M. Nesterov

Authors
  1. Vyacheslav M. Nesterov
    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

Nesterov, V.M. Interval and Twin Arithmetics. Reliable Computing 3, 369–380 (1997). https://doi.org/10.1023/A:1009945403631

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1009945403631

Keywords

Search

Navigation