Verified solving of linear systems with uncertainties in Maple

  • Nelli S. Dimitrova
  • Christian P. Ullrich
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1196)


An algorithm with result verification for linear systems involving uncertainties in the input data is realized for Maple. We give an overview on the collection of procedures designed as a package and report on numerical experiments which confirm the feasibility of implementing such algorithms in computer algebra systems. The package will be made available under the name Velisy for the Maple share library.


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  1. 1.
    Char, B. W., Geddes, K. O., Gonnet, G. H., Leong, B. L., Monagan, M. B., Watt, S. M.: Maple V Language Reference Manual. Springer Verlag (1991)Google Scholar
  2. 2.
    Char, B. W., Geddes, K. O., Gonnet, G. H., Leong, B. L., Monagan, M. B., Watt, S. M.: First Leaves: A Tutorial Introduction to Maple V. Springer Verlag (1992)Google Scholar
  3. 3.
    Maple V Release 3 for DOS and Windows. Getting started. Waterloo Maple Software (1994)Google Scholar
  4. 4.
    Connel, A. E., Corless, R. M.: An Experimental Interval Arithmetic Package in Maple. Interval Computations 2 (1993) 120–134Google Scholar
  5. 5.
    Falcó Korn, C.: Die Erweiterung von Software-Bibliotheken zur effizienten Verifikation der Approximationslösung linearer Gleichungssysteme. PhD Thesis, Institut für Informatik, Universität Basel, Switzerland (1993)Google Scholar
  6. 6.
    Falcó Korn, C., Ullrich, C. P.: Extending LINPACK by Verification Routines for Linear Systems. Mathematics and Computers in Simulation 39 (1995) 21–37Google Scholar
  7. 7.
    Falcó Korn, C., Hörmann, B., Ullrich, C. P.: Verification may be Better than Estimation. To appear in SIAM Journal on Scientific Computing (1996) 6 pagesGoogle Scholar
  8. 8.
    Hammer, R., Hocks, M., Kulisch, U., Ratz, D.: Numerical Toolbox for Verified Computing. Basic Numerical Problems; Theory, Algorithms and Pascal-XSC Programs. Springer Verlag (1993)Google Scholar
  9. 9.
    Neumaier, A.: Interval Methods for Systems of Equations. Cambridge University Press (1990)Google Scholar
  10. 10.
    Rump, S. M.: Inclusion of the Solution of Large Linear Systems with M-matrix. Interval Computations 1(3) (1992) 22–43Google Scholar
  11. 11.
    Stoer, J.: Einführung in die numerische Mathematik I — vierte Auflage. Springer Verlag (1978)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1997

Authors and Affiliations

  • Nelli S. Dimitrova
    • 1
  • Christian P. Ullrich
    • 2
  1. 1.Institute of BiophysicsBulgarian Academy of SciencesSofiaBulgaria
  2. 2.Institute for Computer ScienceUniversity of BaselBaselSwitzerland

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