Skip to main content

Standardized Interval Arithmetic and Interval Arithmetic Used in Libraries

  • Conference paper

Part of the Lecture Notes in Computer Science book series (LNTCS,volume 6327)

Abstract

The standardization of interval arithmetic is currently undertaken by the IEEE-1788 working group. Some features of the standard are detailed. The features chosen here are the ones which may be the less widely adopted in current implementations of interval arithmetic. A survey of interval-based libraries, focusing on these features, is given.

Keywords

  • interval arithmetic
  • standardization
  • interval-based libraries

This is a preview of subscription content, access via your institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   39.99
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   54.99
Price excludes VAT (Canada)
  • 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

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Berz, M., Makino, K.: COSY INFINITY Version 9. Nuclear Instruments and Methods in Physics Research Section A 558(1), 346–350 (2006)

    CrossRef  Google Scholar 

  2. Brisebarre, N., Joldes, M.: Chebyshev Interpolation Polynomial-based Tools for Rigorous Computing. In: ISSAC (2010)

    Google Scholar 

  3. Computer Assisted Proofs in Dynamics, http://capd.ii.uj.edu.pl/

  4. Chabert, G., Jaulin, L.: Contractor programming. Artificial Intelligence 173(11), 1079–1100 (2009)

    CrossRef  MATH  MathSciNet  Google Scholar 

  5. Domes, F.: GloptLab - A configurable framework for the rigorous global solution of quadratic constraint satisfaction problems. Optimization Methods and Software 24(4-5), 727–747 (2009)

    CrossRef  MATH  MathSciNet  Google Scholar 

  6. Goualard, F.: Gaol: NOT Just Another Interval Library (2006-2010)

    Google Scholar 

  7. Goubault, E., Putot, S., Baufreton, P., Gassino, J.: Static Analysis of the Accuracy in Control Systems: Principles and Experiments. In: Leue, S., Merino, P. (eds.) FMICS 2007. LNCS, vol. 4916, pp. 3–20. Springer, Heidelberg (2008)

    CrossRef  Google Scholar 

  8. Granvilliers, L., Benhamou, F.: Algorithm 852: Realpaver: An Interval Solver using Constraint Satisfaction Techniques. ACM TOMS 32(1), 138–156 (2006)

    CrossRef  MathSciNet  Google Scholar 

  9. Hickey, T.J., Ju, Q., van Emden, M.H.: Interval arithmetic: From principles to implementation. Journal of the ACM 48(5), 1038–1068 (2001)

    CrossRef  MathSciNet  Google Scholar 

  10. Hofschuster, W., Krämer, W., Neher, M.: C-XSC and Closely Related Software Packages. In: Cuyt, A., Krämer, W., Luther, W., Markstein, P. (eds.) Numerical Validation in Current Hardware Architectures. LNCS, vol. 5492, pp. 68–102. Springer, Heidelberg (2009)

    CrossRef  Google Scholar 

  11. IEEE Interval Standard Working Group - P1788, http://grouper.ieee.org/groups/1788/

  12. Kearfott, R.B.: GlobSol user guide. Optimization Methods and Software 24(4-5), 687–708 (2009)

    CrossRef  MATH  MathSciNet  Google Scholar 

  13. Knüppel, O.: PROFIL/BIAS A fast interval library. Computing 53(3-4), 277–287 (1994)

    CrossRef  MATH  MathSciNet  Google Scholar 

  14. Krämer, W.: Introduction To The Maple Power Tool Intpakx. In: 12th Int. Conf. on Applications of Computer Algebra. IMI Bulgarian Academy of Sciences, vol. 1(4) (2007)

    Google Scholar 

  15. Lerch, M., Tischler, G., Wolff von Gudenberg, J., Hofschuster, W., Krämer, W.: filib+ +, a Fast Interval Library. ACM TOMS 32(2), 299–324 (2006)

    CrossRef  Google Scholar 

  16. Lin, Y., Stadtherr, M.A.: Validated solution of initial value problems for ODEs with interval parameters. In: Proc. of 2nd Reliable Engineering Computing (2006)

    Google Scholar 

  17. Lohner, R.: Computation of guaranteed enclosures for the solutions of ordinary initial and boundary value problems. In: Computational Ordinary Differential Equations, pp. 425–435. Clarendon Press, Oxford (1992)

    Google Scholar 

  18. Nedialkov, N.S.: Interval Tools for ODEs and DAEs. In: CD-Proc. of the 12th GAMM-IMACS SCAN 2006. IEEE Computer Society, Los Alamitos (2007)

    Google Scholar 

  19. Neumaier, A.: Complete Search in Continuous Global Optimization and Constraint Satisfaction. Acta Numerica, 271–369 (2004)

    Google Scholar 

  20. Papegay, Y., Daney, D., Merlet, J.-P.: Parallel Implementation of Interval Analysis for Equations Solving. In: Dongarra, J., Laforenza, D., Orlando, S. (eds.) EuroPVM/MPI 2003. LNCS, vol. 2840, pp. 555–559. Springer, Heidelberg (2003)

    CrossRef  Google Scholar 

  21. Pryce, J.D., Corliss, G.: Interval Arithmetic with Containment Sets. Computing 78(3), 251–276 (2006)

    CrossRef  MATH  MathSciNet  Google Scholar 

  22. Revol, N., Rouillier, F.: Motivations for an Arbitrary Precision Interval Arithmetic and the MPFI Library. Reliable Computing 11(4), 275–290 (2005)

    CrossRef  MATH  MathSciNet  Google Scholar 

  23. Rump, S.M.: INTLAB - INTerval LABoratory. In: Csendes, T. (ed.) Developments in Reliable Computing, pp. 77–104. Kluwer, Dordrecht (1999)

    Google Scholar 

  24. Sahinides, N.: Baron - Branch And Reduce Optimization Navigator 4.0 (2000)

    Google Scholar 

  25. Sun Studio C., http://docs.sun.com/source/819-3696/iapgCusing.html

  26. van der Hoeven, J., Lecerf, G., Mourrain, B.: Mathemagix (2002), http://www.mathemagix.org

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and Permissions

Copyright information

© 2010 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Revol, N. (2010). Standardized Interval Arithmetic and Interval Arithmetic Used in Libraries. In: Fukuda, K., Hoeven, J.v.d., Joswig, M., Takayama, N. (eds) Mathematical Software – ICMS 2010. ICMS 2010. Lecture Notes in Computer Science, vol 6327. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-15582-6_54

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-15582-6_54

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-15581-9

  • Online ISBN: 978-3-642-15582-6

  • eBook Packages: Computer ScienceComputer Science (R0)