Skip to main content

Intervals

  • Chapter
  • First Online:
Modal Interval Analysis

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 2091))

Abstract

Classical, or set-theoretical intervals [1, 60–62] are a conceptual tool of computation with a sufficiently mature theoretical background to make the development of its techniques of application a major center of interest [33, 44].

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. G. Alefeld, J. Herzberger, Introduction to Interval Computations (Academic, New York, 1983)

    MATH  Google Scholar 

  2. F. Bierbaum, K.P. Schwierz, Moore methods and applications of interval analysis A Bibliography on Interval Mathematics (SIAM, Philadelphia, 1986)

    Google Scholar 

  3. E. Gardenyes, M.A. Sainz, L. Jorba, R. Calm, R. Estela, H. Mielgo, A. Trepat, Modal intervals. Reliable Comput. 7(2), 77–111 (2001)

    Article  Google Scholar 

  4. E. Hansen, Global Optimization Using Interval Analysis (Marcel Dekker, New York, 1992)

    MATH  Google Scholar 

  5. L. Jaulin, M. Kieffer, O. Didrit, E. Walter, Applied Interval Analysis: With Examples in Parameter and State Estimation, Robust Control and Robotics (Springer, London, 2001)

    Book  Google Scholar 

  6. E. Kaucher, Algebraische orweiterungen der intervallrechnung unter erhaltung der ordnungs und verbandsstrukturen. Comput. Suppl. 1, 65–79 (1977)

    Article  Google Scholar 

  7. E. Kaucher, Interval analysis in the extended interval space IR. Comput. Suppl. 2, 33–49 (1979)

    Article  MathSciNet  Google Scholar 

  8. V. Kreinovich, Why intervals? A simple limit theorem that is similar to limit theorems from statistics. Reliable Comput. 1(1), 33–40 (1995)

    MathSciNet  MATH  Google Scholar 

  9. R.E. Moore, Interval arithmetic and automatic error analysis in digital computing. Ph.D. thesis, Stanford University, USA, 1962

    Google Scholar 

  10. R.E. Moore, Interval analysis (Prentice-Hall, Englewood Cliffs, 1966)

    MATH  Google Scholar 

  11. R.E. Moore, Methods and Applications of Interval Analysis (Studies in Applied Mathematics (SIAM), Philadelphia, 1979)

    Google Scholar 

  12. M. Nogueira, A. Nandigam, Why intervals? because if we allow other sets, tractable problems become intractable. Reliable Comput. 1(4), 389–394 (1998)

    Article  MathSciNet  Google Scholar 

  13. S. Ratschan, Applications of quantified constraint solving (2002). http://www.mpi-sb.mpg.de/~ratschan/appqcs.html

  14. A. Trepat, Completación reticular del espacio de intervalos. Ph.D. thesis, Facultad de Matemáticas, Universidad de Barcelona, Spain, 1982

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

Copyright information

© 2014 Springer International Publishing Switzerland

About this chapter

Cite this chapter

Sainz, M.A., Armengol, J., Calm, R., Herrero, P., Jorba, L., Vehi, J. (2014). Intervals. In: Modal Interval Analysis. Lecture Notes in Mathematics, vol 2091. Springer, Cham. https://doi.org/10.1007/978-3-319-01721-1_1

Download citation

Publish with us

Policies and ethics