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.
This work was supported in part by EPSRC Grant D033373/1.
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References
Moore, R.E.: Methods and Applications of Interval Analysis. SIAM, Philadelphia (1979)
Neumaier, A.: Interval Methods for Systems of Equations. Cambridge University Press, Cambridge (1990)
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/
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++
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)
GSL: GNU Scientific Library (1996 - June 2004), http://www.gnu.org/software/gsl/
Klatte, R., Kulisch, U., Wiethoff, A., Lawo, C., Rauch, M.: C–XSC – A C++ Library for Extended Scientific Computing. Springer, Heidelberg (1993)
Hammer, R., Hocks, M., Kulisch, U., Ratz, D.: Numerical Toolbox for Verified Computing I — Basic Numerical Problems. Springer, Heidelberg (1993)
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)
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)
Pryce, J.D., Corliss, G.F.: Interval arithmetic with containment sets. Computing 78(3), 251–276 (2006)
Rump, S.M.: INTLAB interval toolbox, version 5.2 (1999–2006), http://www.ti3.tu-harburg.de/intlab.ps.gz
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)
Knüppel, O.: PROFIL/BIAS – A fast interval library. Computing 53(3–4), 277–287 (1994), http://www.ti3.tu-harburg.de/profil_e
Knüppel, O.: PROFIL/BIAS v 2.0. Bericht 99.1, Technische Universität Hamburg-Harburg, Harburg, Germany (1999)
Brönnimann, H., Melquiond, G., Pion, S.: The Boost interval arithmetic library (2006), http://www.cs.utep.edu/interval-comp/main.html
Goualard, F.: Gaol, not just another interval library (2006), http://www.sourceforge.net/projects/gaol/
Hofschuster, W.: C–XSC – A C++ Class Library web page (2004) http://www.math.uni-wuppertal.de/wrswt/xsc/cxsc.html
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)
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)
Sun Microsystems.: C++ interval arithmetic programming reference (2004–2006) http://docs.sun.com/db/doc/806-7998
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/ .
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)
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
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)
Neumaier, A.: COCONUT Web page (2001-2003), http://www.mat.univie.ac.at/~neum/glopt/coconut
Kreinovich, V.: Interval Computations (2006), http://www.cs.utep.edu/interval-comp/main.html
Parnas, D.L.: Software Fundamentals: Collected Papers by David L. Parnas. Addison-Wesley, Reading (2001)
Knuth, D.E.: Literate programming. The Computer Journal 27(2), 97–111 (1984)
LiterateProgramming: Literate Programming Web page (2000–2005), http://www.literateprogramming.com/
Burke, E.M., Coyner, B.M.: Java Extreme Programming Cookbook. O’Reilly, Sebastopol (2003)
Beck, K.: Test-Driven Development: By Example. Addison-Wesley, Reading (2003)
Hull, T., Enright, W., Fellen, B., Sedgwick, A.: Comparing numerical methods for ordinary differential equations. SIAM J. Numer. Anal. 9, 603–637 (1972)
Mazzia, F., Iavernaro, F., Magherini, C.: Test set for IVP solvers, release 2.2 (2003), http://pitagora.dm.uniba.it/~testset/
Pryce, J.D.: A test package for Sturm-Liouville solvers. ACM Trans. Math. Software 25(1), 21–57 (1999)
Pryce, J.D.: Algorithm 789: SLTSTPAK, a test package for Sturm-Liouville solvers. ACM Trans. Math. Software 25(1), 58–69 (1999)
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)
Kirchner, R., Kulisch, U.W.: Hardware support for interval arithmetic. Reliable Computing 12(3), 225–237 (2006)
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Corliss, G.F., Kearfott, R.B., Nedialkov, N., Pryce, J.D., Smith, S. (2008). Interval Subroutine Library Mission. In: Hertling, P., Hoffmann, C.M., Luther, W., Revol, N. (eds) Reliable Implementation of Real Number Algorithms: Theory and Practice. Lecture Notes in Computer Science, vol 5045. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-85521-7_2
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