Interval Subroutine Library Mission

  • George F. Corliss
  • R. Baker Kearfott
  • Ned Nedialkov
  • John D. Pryce
  • Spencer Smith
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5045)

Abstract

We propose the collection, standardization, and distribution of a full-featured, production quality library for reliable scientific computing with routines using interval techniques for use by the wide community of applications developers.

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References

  1. 1.
    Moore, R.E.: Methods and Applications of Interval Analysis. SIAM, Philadelphia (1979)MATHGoogle Scholar
  2. 2.
    Neumaier, A.: Interval Methods for Systems of Equations. Cambridge University Press, Cambridge (1990)MATHGoogle Scholar
  3. 3.
    Fong, K., Jefferson, T., Suyehiro, T., Walton, L.: Guide to the SLATEC common mathematical library. Technical report (1990), netlib.org, http://www.netlib.org/slatec/
  4. 4.
    Press, W.H., Flannery, B.P., Teukolsky, S.A., Vetterling, W.T.: Numerical Recipes in Fortran: The Art of Scientific Computing, 2nd edn. Cambridge University Press, Cambridge (1992); Also available for Fortran 90, C, and C++ Google Scholar
  5. 5.
    Press, W.H., Teukolsky, S.A., Vetterling, W.T., Flannery, B.P.: Numerical Recipes in C++: The Art of Scientific Computing, 2nd edn. Cambridge University Press, Cambridge (2002)Google Scholar
  6. 6.
    GSL: GNU Scientific Library (1996 - June 2004), http://www.gnu.org/software/gsl/
  7. 7.
    Klatte, R., Kulisch, U., Wiethoff, A., Lawo, C., Rauch, M.: C–XSC – A C++ Library for Extended Scientific Computing. Springer, Heidelberg (1993)Google Scholar
  8. 8.
    Hammer, R., Hocks, M., Kulisch, U., Ratz, D.: Numerical Toolbox for Verified Computing I — Basic Numerical Problems. Springer, Heidelberg (1993)MATHGoogle Scholar
  9. 9.
    Lerch, M., Tischler, G., von Gudenberg, J.W., Hofschuster, W., Krämer, W.: filib++, a fast interval library supporting containment computations. ACM Transactions on Mathematical Software 32(2) (2006)Google Scholar
  10. 10.
    Lerch, M., Tischler, G., Wolff von Gudenberg, J., Hofschuster, W., Krämer, W.: The interval library filib++ 2.0 - design, features and sample programs (preprint 2001/4), Universität Wuppertal, Wuppertal, Germany (2001)Google Scholar
  11. 11.
    Pryce, J.D., Corliss, G.F.: Interval arithmetic with containment sets. Computing 78(3), 251–276 (2006)MATHCrossRefMathSciNetGoogle Scholar
  12. 12.
    Rump, S.M.: INTLAB interval toolbox, version 5.2 (1999–2006), http://www.ti3.tu-harburg.de/intlab.ps.gz
  13. 13.
    Brönnimann, H., Melquiond, G., Pion, S.: A proposal to add interval arithmetic to the C++ standard library. Technical Report N1843-05-0103, CIS Department, Polytechnic University, New York, and Laboratoire de l’Informatique du Parallélisme, École Normale Supérieure de Lyon, and INRIA Sophia Antipolis (2005–2006)Google Scholar
  14. 14.
    Knüppel, O.: PROFIL/BIAS – A fast interval library. Computing 53(3–4), 277–287 (1994), http://www.ti3.tu-harburg.de/profil_e MATHCrossRefMathSciNetGoogle Scholar
  15. 15.
    Knüppel, O.: PROFIL/BIAS v 2.0. Bericht 99.1, Technische Universität Hamburg-Harburg, Harburg, Germany (1999)Google Scholar
  16. 16.
    Brönnimann, H., Melquiond, G., Pion, S.: The Boost interval arithmetic library (2006), http://www.cs.utep.edu/interval-comp/main.html
  17. 17.
    Goualard, F.: Gaol, not just another interval library (2006), http://www.sourceforge.net/projects/gaol/
  18. 18.
    Hofschuster, W.: C–XSC – A C++ Class Library web page (2004) http://www.math.uni-wuppertal.de/wrswt/xsc/cxsc.html
  19. 19.
    Hofschuster, W., Krämer, W.: C–XSC 2.0: A C++ library for extended scientific computing. In: Alt, R., Frommer, A., Kearfott, R.B., Luther, W. (eds.) Dagstuhl Seminar 2003. LNCS, vol. 2991, pp. 15–35. Springer, Heidelberg (2004)Google Scholar
  20. 20.
    Hofschuster, W., Krämer, W., Wedner, S., Wiethoff, A.: C–XSC 2.0: A C++ library for extended scientific computing. Preprint BUGHW–WRSWT 2001/1, Universität Wuppertal (2001)Google Scholar
  21. 21.
    Sun Microsystems.: C++ interval arithmetic programming reference (2004–2006) http://docs.sun.com/db/doc/806-7998
  22. 22.
    Anderson, E., Bai, Z., Bischof, C., Blackford, S., Demmel, J., Dongarra, J., Du Croz, J., Greenbaum, A., Hammarling, S., McKenney, A., Sorensen, D.: LAPACK User’s Guide, 3rd edn. SIAM, Philadelphia (1999); Certain derivative work portions have been copyrighted by the Numerical Algorithms Group Ltd. http://www.netlib.org/lapack/, http://www.nacse.org/demos/lapack/. MATHGoogle Scholar
  23. 23.
    Balay, S., Buschelman, K., Eijkhout, V., Gropp, W.D., Kaushik, D., Knepley, M.G., McInnes, L.C., Smith, B.F., Zhang, H.: PETSc users manual. Technical Report ANL-95/11 - Revision 2.1.5, Argonne National Laboratory (2004)Google Scholar
  24. 24.
    Balay, S., Buschelman, K., Gropp, W.D., Kaushik, D., Knepley, M.G., McInnes, L.C., Smith, B.F., Zhang, H.: PETSc Web page (2001), http://www.mcs.anl.gov/petsc
  25. 25.
    Balay, S., Gropp, W.D., McInnes, L.C., Smith, B.F.: Efficient management of parallelism in object oriented numerical software libraries. In: Arge, E., Bruaset, A.M., Langtangen, H.P. (eds.) Modern Software Tools in Scientific Computing, pp. 163–202. Birkhäuser Press (1997)Google Scholar
  26. 26.
    Neumaier, A.: COCONUT Web page (2001-2003), http://www.mat.univie.ac.at/~neum/glopt/coconut
  27. 27.
    Kreinovich, V.: Interval Computations (2006), http://www.cs.utep.edu/interval-comp/main.html
  28. 28.
    Parnas, D.L.: Software Fundamentals: Collected Papers by David L. Parnas. Addison-Wesley, Reading (2001)Google Scholar
  29. 29.
    Knuth, D.E.: Literate programming. The Computer Journal 27(2), 97–111 (1984)MATHCrossRefGoogle Scholar
  30. 30.
    LiterateProgramming: Literate Programming Web page (2000–2005), http://www.literateprogramming.com/
  31. 31.
    Burke, E.M., Coyner, B.M.: Java Extreme Programming Cookbook. O’Reilly, Sebastopol (2003)Google Scholar
  32. 32.
    Beck, K.: Test-Driven Development: By Example. Addison-Wesley, Reading (2003)Google Scholar
  33. 33.
    Hull, T., Enright, W., Fellen, B., Sedgwick, A.: Comparing numerical methods for ordinary differential equations. SIAM J. Numer. Anal. 9, 603–637 (1972)MATHCrossRefMathSciNetGoogle Scholar
  34. 34.
    Mazzia, F., Iavernaro, F., Magherini, C.: Test set for IVP solvers, release 2.2 (2003), http://pitagora.dm.uniba.it/~testset/
  35. 35.
    Pryce, J.D.: A test package for Sturm-Liouville solvers. ACM Trans. Math. Software 25(1), 21–57 (1999)MATHCrossRefMathSciNetGoogle Scholar
  36. 36.
    Pryce, J.D.: Algorithm 789: SLTSTPAK, a test package for Sturm-Liouville solvers. ACM Trans. Math. Software 25(1), 58–69 (1999)MATHCrossRefMathSciNetGoogle Scholar
  37. 37.
    Corliss, G.F., Yu, J.: Testing COSY’s interval and Taylor model arithmetic. In: Alt, R., Frommer, A., Kearfott, R.B., Luther, W. (eds.) EDBT 2004. LNCS, vol. 2992, pp. 91–105. Springer, Heidelberg (2004)Google Scholar
  38. 38.
    Kirchner, R., Kulisch, U.W.: Hardware support for interval arithmetic. Reliable Computing 12(3), 225–237 (2006)MATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • George F. Corliss
    • 1
  • R. Baker Kearfott
    • 2
  • Ned Nedialkov
    • 3
  • John D. Pryce
    • 4
  • Spencer Smith
    • 5
  1. 1.Marquette University 
  2. 2.University of Louisiana at Lafayette 
  3. 3.McMaster University and Lawrence Livermore National Laboratory 
  4. 4.Cranfield University, RMCS Shrivenham 
  5. 5.McMaster University 

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