Skip to main content

INTLAB — INTerval LABoratory

  • Chapter

Abstract

INTLAB is a toolbox for Matlab supporting real and complex intervals, and vectors, full matrices and sparse matrices over those. It is designed to be very fast. In fact, it is not much slower than the fastest pure floating point algorithms using the fastest compilers available (the latter, of course, without verification of the result). Beside the basic arithmetical operations, rigorous input and output, rigorous standard functions, gradients, slopes and multiple precision arithmetic is included in INTLAB. Portability is assured by implementing all algorithms in Matlab itself with exception of exactly one routine for switching the rounding downwards, upwards and to nearest. Timing comparisons show that the used concept achieves the anticipated speed with identical code on a variety of computers, ranging from PC’s to parallel computers. INTLAB is freeware and may be copied from our home page.

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

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD   109.99
Price excludes VAT (USA)
  • Durable hardcover 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. J.P. Abbott and R.P. Brent. Fast Local Convergence with Single and Multistep Methods for Nonlinear Equations. Austr. Math. Soc. 19 (Series B), pages 173–199, 1975.

    Google Scholar 

  2. ACRITH High–Accuracy Arithmetic Subroutine Library, Program Description and User’s Guide. IBM Publications, No. SC 33–6164–3, 1986.

    Google Scholar 

  3. G. Alefeld and J. Herzberger. Introduction to Interval Computations. Academic Press, New York, 1983.

    MATH  Google Scholar 

  4. E. Anderson, Z. Bai, C. Bischof, J. Demme], J. Dongarra, J. Du Croz, A. Greenbaum, S. Ham-marling, A. McKenney, S. Ostrouchov, and Sorensen D.C. LAPACK User’s Guide, Resease 2.0. SIAM Publications, Philadelphia, second edition edition, 1995.

    Google Scholar 

  5. ARITHMOS, Benutzerhandbuch, Siemens AG, Bibl.-Nr. U 2900-I-Z87–1 edition, 1986.

    Google Scholar 

  6. J.J. Dongarra, J.J. Du Croz, I.S. Duff, and S.J. Hammarling. A set of level 3 basic linear algebra subprograms. ACM Trans. Math. Software, 16: 1–17, 1990.

    Article  MATH  Google Scholar 

  7. J.J. Dongarra, J.J. Du Croz, S.J. Hammarling, and R.J. Hanson. An extended set of Fortran basic linear algebra subprograms. ACM Trans. Math. Software, 14 (1): 1–17, 1988.

    Article  MATH  Google Scholar 

  8. D. Husung. ABACUS - Programmierwerkzeug mit hochgenauer Arithmetik für Algorithmen mit verifizierten Ergebnissen. Diplomarbeit, Universität Karlsruhe, 1988.

    Google Scholar 

  9. D. Husung. Precompiler for Scientific Computation (TPX). Technical Report 91. 1, Inst. f. Informatik III, TU Hamburg-Harburg, 1989.

    Google Scholar 

  10. ANSI/IEEE 754–1985, Standard for Binary Floating-Point Arithmetic, 1985.

    Google Scholar 

  11. R.B. Kearfott, M. Dawande, K. Du, and C. Hu. INTLIB: A portable Fortran-77 elementary function library. Interval Comput., 3 (5): 96–105, 1992.

    Google Scholar 

  12. R.B. Kearfott, M. Dawande, and C. Hu. INTLIB: A portable Fortran-77 interval standard function library. ACM Trans. Math. Software, 20: 447–459, 1994.

    Article  MATH  Google Scholar 

  13. R. Klatte, U. Kulisch, M. Neaga, D. Ratz, and Ch. Ullrich. PASCAL-XSC - Sprachbeschreibung mit Beispielen. Springer, 1991.

    Google Scholar 

  14. O. Knüppel. PROFIL/BIAS–A Fast Interval Library. Computing, 53: 277–287, 1994.

    Article  MathSciNet  MATH  Google Scholar 

  15. O. Knüppel. PROFIL/BIAS and extensions, Version 2. 0. Technical report, Inst. f. Informatik III, Technische Universität Hamburg-Harburg, 1998.

    Google Scholar 

  16. R. Krawczyk. Newton-Algorithmen zur Bestimmung von Nullstellen mit Fehlerschranken. Computing, 4: 187–201, 1969.

    Article  MathSciNet  MATH  Google Scholar 

  17. R. Krier. Komplexe Kreisarithmetik. PhD thesis, Universität Karlsruhe, 1973.

    Google Scholar 

  18. C. Lawo. C-XSC, a programming environment for verified scientific computing and numerical data processing. In E. Adams and U. Kulisch, editors, Scientific computing with automatic result verification, pages 71–86. Academic Press, Orlando, Fla., 1992.

    Google Scholar 

  19. C.L. Lawson, R.J. Hanson, D. Kincaid, and F.T. Krogh. Basic Linear Algebra Subprograms for FORTRAN usage. ACM Trans. Math. Soft., 5: 308–323, 1979.

    Article  MATH  Google Scholar 

  20. R.E. Moore. A Test for Existence of Solutions for Non-Linear Systems. SIAM J. Numer. Anal. 4, pages 611–615, 1977.

    Article  Google Scholar 

  21. A. Neumaier. Interval Methods for Systems of Equations. Encyclopedia of Mathematics and its Applications. Cambridge University Press, 1990.

    MATH  Google Scholar 

  22. S. Oishi. private communication, 1998.

    Google Scholar 

  23. S.M. Rump. Kleine Fehlerschranken bei Matrixproblemen. PhD thesis, Universität Karlsruhe, 1980.

    MATH  Google Scholar 

  24. S.M. Rump. Validated Solution of Large Linear Systems. In R. Albrecht, G. Alefeld, and H.J. Steter, editors, Computing Supplementum, volume 9, pages 191–212. Springer, 1993.

    Google Scholar 

  25. S.M. Rump. Fast and parallel interval arithmetic. BIT, 39 (3): 539–560, 1999.

    Article  MathSciNet  Google Scholar 

  26. T. Sunaga. Theory of an Interval Algebra and its Application to Numerical Analysis. RAAG Memoirs, 2: 29–46, 1958.

    Google Scholar 

  27. J. Zemke. b4m - BIAS for Matlab. Technical report, Inst. f. Informatik III, Technische Universität Hamburg-Harburg, 1998.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1999 Springer Science+Business Media Dordrecht

About this chapter

Cite this chapter

Rump, S.M. (1999). INTLAB — INTerval LABoratory. In: Csendes, T. (eds) Developments in Reliable Computing. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-1247-7_7

Download citation

  • DOI: https://doi.org/10.1007/978-94-017-1247-7_7

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-90-481-5350-3

  • Online ISBN: 978-94-017-1247-7

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics