Parametric Linear Interval Systems

Institutions involved in the project:
 

	Scientific Computing / Software Engineering Faculty C / Department of Mathematics University of Wuppertal (BUW) Germany
	Bulgarian Academy of Sciences (BAS) Institute of Mathematics and Informatics Bulgaria

The bilateral project "Parametric Linear Interval Systems" is funded by Deutsche Forschungsgemeinschaft (DFG) and  Bulgarian National Science Fund under grants No I-903/99 and MM-1301/2003.

Principal investigators:

Bulgarian Academy of Sciences, Sofia
Institute of Mathematics and Informatics
Section "Biomathematics
Assoc. Prof. Dr. Evgenija D. Popova

and

Bergische Universität Wuppertal (BUW),
FB C, Fachgruppe Mathematik,
Prof. Dr. Walter Krämer

Exchange of experts:

• Prof. Dr. Walter Krämer, April 2002 in Sofia/Borovetz
• Assoc. Prof. Dr. Evgenija D. Popova, June/July 2003 in Wuppertal
• M.Sc. Hassan El-Owny, April 2004 in Sofia/Borovetz
• Assoc. Prof. Dr. Evgenija D. Popova, May 2004 in Wuppertal
• Prof. Dr. Walter Krämer, June 2006 in Bulgaria
• Special Session on ACA-2006 (International Conference on Applications of Computer Algebra), June 26-29, 2006, Varna, Bulgaria: "Computer Algebra and Interval Computations."
  (Organizers: E. Popova & W. Krämer)
• Assoc. Prof. Dr. Evgenija D. Popova, September/October 2006 in Wuppertal
• Assoc. Prof. Dr. Evgenija D. Popova, May 2008 in Wuppertal
• Special Session at ACA'08 (14th International Conference on Applications of Computer Algebra), July 27-30, 2008, RISC Institute, Castle of Hagenberg, Linz, Austria (Organizers: W. Krämer, E. Popova).
• Special Session at ACA'09 (15th International Conference on Applications of Computer Algebra), June 25-28, 2009, Ecole de technologie superieure (ETS), Montreal, Quebec, Canada (Organizers: W. Krämer, M. Neher, E. Popova).
• Prof. Dr. Walter Krämer, Int. Workshop on Mathematical Modelling and Scientific Computing, Sept. 23-26, 2009, Velingrad, Bulgaria.
• Assoc. Prof. Dr. Evgenija D. Popova, October/November 2009 in Wuppertal
• Assoc. Prof. Dr. Evgenija D. Popova, May/June 2010 in Wuppertal
• Special Session at ACA'10 (16th International Conference on Applications of Computer Algebra), June 24-27, 2010, Vlora, Albania (Organizers: W. Krämer, M. Neher, E. Popova).

Papers and Preprints:

• Popova, E.; Krämer, W.; Russev, M.:
  Integration of C-XSC Automatic Differentiation in Mathematica
  Preprint 3/2010, IMI-BAS, Sofia, 2010 ().
• Popova, E.; Kolev, L.; Krämer, W.:
  A Solver for Complex-Valued Parametric Linear Systems
  Serdica Journal of Computing 4(1), p. 123-132, 2010.
• Krämer, W.:
  Computer-Assisted Proofs and Symbolic Computations
  Serdica Journal of Computing 4(1), p. 73-84, 2010.
• Popova, E.:
  Mathematica Connectivity to Interval Libraries filib++ and C-XSC
  In Cuyt, A. et al. (eds.), Numerical Validation. LNCS 5492, Springer, Heidelberg, p. 117-132, 2009. ().
• Krämer, W.; Popova, E. D.:
  Visualizing Parametric Solution Sets (extended version)
  Preprint BUW-WRSWT 2007/6, Universität Wuppertal, 2007
  Published in: BIT Numerical Mathematics 48(1):95-115, 2008. ( (860 KB))
• Krämer, W.; Popova, E. D.:
  Visualizing Parametric Solution Sets
  Preprint BUW-WRSWT 2006/10, Universität Wuppertal, 2006
• Krämer, W.:
  Generalized Intervals and the Dependency Problem.
  Preprint BUW-WRSWT 2006/4, Universität Wuppertal, 2006 ( (120 KB))
  Published in: PAMM - Proceedings in Applied Mathematics and Mechanics,
  Vol. 6, Nr. 1, p. 685-686, Wiley-InterScience (2006).
• Krämer, W.; Popova, E. D.:
  Inner and Outer Bounds for the Solution Set of Parametric Linear Systems
  Preprint BUW-WRSWT 2006/6, Universität Wuppertal, 2006 ( (215 KB))
  Published in: Journal of Computational and Applied Mathematics, Vol. 199, Issue 2, February 2007, pages 310 - 316.
• Krämer, W.:
  Computing and Visualizing Solution Sets of Interval Linear Systems.
  Preprint BUW-WRSWT 2006/8, Universität Wuppertal, 2006 ( (320 KB))
  Accepted for publication in a special issue of Serdica Journal of Computing (ACA'06), 2007.
• Krämer, W.; Popova, E. D.:
  Zur Berechnung von verlässlichen Außen- und Inneneinschließungen bei parameterabhängigen linearen Gleichungssystemen
  Preprint BUW-WRSWT 2004/2, Universität Wuppertal, 2004 (Postscript (46 KB), PDF (34 KB))
  Published in: PAMM - Proceedings in Applied Mathematics and Mechanics,
  Vol. 4, Nr. 1, p. 670-671, Wiley-InterScience (2004).
• Popova, E. D.; Krämer, W.:
  Parametric Fixed-Point Iteration Implemented in C-XSC
  Preprint BUW-WRSWT 2003/3, Universität Wuppertal, 2003 (Update May 2004) (Postscript (1380 KB), PDF (325 KB))

Software:

• ADExpressions: Software Communicating Functional Expressions from Mathematica to C-XSC Automatic Differentiation Objects.
  • Readme: ADExpressions.readme.txt
  • Documentation: Preprint 3/2010, IMI-BAS ()
  • Software Download: ADExpressions.zip
• Software Embedding C-XSC Modules for Automatic Differentiation in Mathematica.
  • Documentation: Preprint 3/2010, IMI-BAS ()
  • Software Download: ADpackages.zip
• Software Embedding C-XSC Modules for nonlinear problem-solving in Mathematica.
  • Documentation: Preprint 3/2010, IMI-BAS ()
  • Software Download: nlADproblems.zip
• Solving Parametric Interval Linear Systems (ParLinSys)