E.D.Popova
Selected Papers on Interval Mathematics & Computing

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General Investigations

  1. Popova, E. and W. Kraemer: Visualizing Parametric Solution Sets, BIT Numerical Mathematics 48(1): 95-115, 2008, online Jan. 24, 2008. (Abstract, DOI:10.1007/s10543-007-0159-3)

  2. Popova, E.: Computer-Assisted Proofs in Solving Linear Parametric Problems, in the Proceedings of SCAN'06, p. 35, IEEE Computer Society Press, 2006. (Abstract) Click here to request a full text Reprint.
    -- Proven monotonicity properties for a benchmark example - (text - PDF, data - ASCII)

  3. Popova, E., R. Iankov, Z. Bonev: Bounding the Response of Mechanical Structures with Uncertainties in all the Parameters. In R.L.Muhannah, R.L.Mullen (Eds): Proceedings of the NSF Workshop on Reliable Engineering Computing (REC), Svannah, Georgia USA, Feb. 22-24, 2006, 245-265. (Full Text - PDF 352K)
    -- FEM model of a two-bay two-story steel frame - 2 benchmark examples (links to the corresponding data files are available in the PDF file)

  4. Popova, E.: Improved Solution Enclosures for Over- and Underdetermined Interval Linear Systems. In Lirkov, I., S. Margenov, J. Wasniewski (Eds.): Proceedings of LSSC 2005, Lecture Notes in Computer Science 3743, pp. 305-312, 2006. (Abstract, Full Text - PDF 356K)

  5. Popova, E.: Solving Linear Systems whose Input Data are Rational Functions of Interval Parameters.
    In: T. Boyanov et al. (Eds.) Numerical Methods and Applications, LNCS 4310, 2007, Springer Berlin/Heidelberg, 345-352. (Abstract)
    Expanded version in: Preprint No. 3/2005, Institute of Mathematics and Informatics, BAS, Sofia, December 2005. (Full Text - PDF 550K)

  6. Popova, E. and W. Kraemer: Inner and Outer Bounds for Parametric Linear Systems. J. Computational and Applied Mathematics 199(2), 2007, 310-316. (Abstract)

  7. Popova, E.: Generalizing the Parametric Fixed-Point Iteration. Proceedings in Applied Mathematics & Mechanics (PAMM) 4, issue 1, 2004, pp. 680-681. (Abstract, Full Text - PDF and PS)

  8. Popova, E.: Strong Regularity of Parametric Interval Matrices. Mathematics & Education in Mathematics, 2004, (Eds. I. Dimovski et al.), BAS, pp. 446-451. (Full Text - PDF and PS)

  9. Popova, E.: Parametric Interval Linear Solver. Numerical Algorithms 37 (1-4), 2004, 345-356. (Abstract, Full Text - PDF)

  10. Popova, E.; Datcheva, M.; Iankov, R.; Schanz, T.: Mechanical Models with Interval Parameters. In: K. Guerlebeck, L. Hempel, C. Koenke (Eds.) IKM2003: Digital Proceedings of 16th International Conference on the Applications of Computer Science and Mathematics in Architecture and Civil Engineering, ISSN 1611-4086, Bauhaus University Weimar, 2003. ( Full Text - PDF)

  11. Popova, E.; Datcheva, M.; Iankov, R.; Schanz, T.: Sharp Bounds for Strains and Stresses in Uncertain Mechanical Models. I. Lirkov et al. (Eds): LSSC 2003, Lecture Notes in Computer Science 2907, pp. 262-269, 2004. (Abstract, Full Text - 265K PDF)

  12. Popova, E. D.: Quality of the Solution Sets of Parameter Dependent Interval Linear Systems.  ZAMM 82 (2002) 10, pp. 723-727. (Abstract, Full Text - 160K PDF)

  13. Popova, E. D.: On the Solution of Parametrised Linear Systems. In: W. Kraemer, J. Wolff von Gudenberg (Eds.): Scientific Computing, Validated Numerics, Interval Methods. Kluwer Acad. Publishers, 2001, pp. 127-138. (Full Text - PS 151K, PDF 200K)

  14. Popova, E. D.: Multiplication Distributivity of Proper and Improper Intervals. Reliable Computing 7, 2, 2001, pp.129-140. (Abstract, Full Text - 142K PostScript)

  15. Popova, E. D.: All about Generalized Interval Distributive Relations. I. Complete Proof of the Relations. Sofia, March 2000. (Abstract, Full Text - 389K PostScript)

  16. Popova, E. D.: Algebraic Solutions to a Class of Interval Equations Journal of Universal Computer Science, Vol. 4, no. 1, 1998, pp. 48-67. (Abstract, Full Text - 250K PostScript)

  17. Markov, S. M.; Popova, E. D.; Ullrich, C.: On the Solution of Linear Algebraic Equations Involving Interval Coefficients. In S. Margenov, P. Vassilevski (Eds.): Iterative Methods in Linear Algebra, II, IMACS Series in Computational and Applied Mathematics, 3 1996, pp. 216-225. (Abstract, Full Text - 130K PostScript)

  18. Dimitrova, N.; Markov, S. M.; Popova, E. D.: Extended Interval Arithmetics: New Results and Applications. In Atanassova, L.; Herzberger, J. (Eds.): Computer Arithmetic and Enclosure Methods. Elsevier Sci. Publishers B. V., 1992, pp. 225-232. (Abstract, Full Text - PDF 132K, PS 266K)

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    Interval Interpolation & Approximation

  19. Markov, S. M.; Popova, E. D.: Estimation and Identification using Interval Arithmetic Proceedings of 9th IFAC/IFORS Symposium on Identification and System Parameter Estimation, Pergamon Press, 1991, pp. 769-772. (Full Text - 78K PostScript)

  20. Markov, S. M.; Popova, E. D.: New Aspects of Mathematical Modelling: Curve Fitting Mathematical Modelling and Scientific Computations, A.Andreev, I.Dimov, S. Markov, Ch. Ullrich (Eds.), Publishing House of the Bulg. Acad. of Sci., Sofia, 1991, pp.49-63.

  21. Markov, S. M.; Popova, E. D.: Curve Fitting under Interval Data for the Measurements: Software Tools and Numerical Examples Mathematics and Mathematical Education, BAS, Sofia, 1992, pp. 322-332.

  22. Akyildiz, Y.; Markov, S. M.; Popova, E. D.; Schulze, J.: Computer-Aided Interval Interpolation Advances in Numerical Methods and Applications, World Scientific, Singapore, 1994, pp. 3-10.

  23. Akyildiz, Y.; Markov, S. M.; Miller, J.; Popova, E. D.: Computational Tools for Interpolation and Curve Fitting under Uncertainties Hellenic European Research on Mathematics and Informatics'94, Athens, pp. 659-666.

  24. Markov, S. M.; Popova, E. D.: Interpolation and Estimation using Interval Arithmetic Bounding Approaches to System Identification, Milanese, M.; Norton, J. P.; Piet-Lahanier, H.; Walter, E. (Eds.), Plenum Press, London, N.Y., 1996, pp. 139-157. (Full Text - PDF and PS)

  25. Markov, S. M.; Popova, E. D.; Schneider, U.; Schulze, J.: On Linear Interpolation under Interval Data Mathematics and Computers in Simulation vol. 42, 1, 1996, pp. 35-45. (Full Text - 179K PostScript)

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    Interval Specification & Implementations

  26. Popova, E. D.: On the Interoperability Between Interval Software. In: Numerical Validation in Current Hardware Architectures, number 08021 in Dagstuhl Seminar Proceedings, Internationales Begegnungs- und Forschungszentrum fuer Informatik (IBFI), Schloss Dagstuhl, Germany, 2008. (Full Text - PDF 380 K, with an electronic supplement PDF and a source archive zip)

  27. Popova, E. D.; Krämer, W.: Parametric Fixed-Point Iteration Implemented in C-XSC. Preprint BUW-WRSWT 2003/3, Universität Wuppertal, 2003. (Full Text - PostScript 1380 K, PDF 325 K)

  28. E. Popova: On the Efficiency of Interval Multiplication Algorithms. Proceedings of III-rd International Conference ``Real Numbers and Computers'', Paris, April 27-29, 1998, 117-132. (Full Text - 180K PDF)

  29. Popova, E. D.; Ullrich, C.: Generalising BIAS Specification Journal of Universal Computer Science, Vol. 3, no. 1, 1997, pp. 23-41. (Abstract, Full Text - 218K PostScript)

  30. Popova, E. D.; Markov, S. M.: Towards Credible Implementation of Inner Interval Operations 15th IMACS World Congress on Scientific Computation, Modelling and Applied Mathematics. Volume 2 Numerical Mathematics, 1997, pp. 371-376. (Abstract, Full Text - 92K PostScript)

  31. Popova, E. D.: Interval Operations Involving NaNs Reliable Computing, 2 (2), 1996, pp. 161-165. (Abstract, Full Text 27K PostScript)

  32. Popova, E. D.: Extended Interval Arithmetic in IEEE Floating-Point Environment. Interval Computations, No 4, 1994, pp. 100-129. (Abstract, Full Text - PDF 198K, PS 377K)

  33. Popova, E. D.: On a Formally Correct Implementation of IEEE Computer Arithmetic Journal of Universal Computer Science, Vol. 1, No. 7, 1995, pp. 556-565. (Abstract) Full Text - 88K PostScript)

  34. R. Angelov, P. Bochev, G. Grozev, N. Kjurkchiev, L. Malahova, S. Markov, E. Popova, B. Stojanova, T. Vassilevska, P. Vassilevski: HIFICOMP: Subroutine library for HIghly efFIcient and accurate COMPutations, Methodological guide. Center for Informatics and Computer Technology, Bulgarian Academy of Sciences, 1987, CINTI Reg.No.1.A.066.02112-01 37

  35. R. Angelov, P. Bochev, G. Grozev, N. Kjurkchiev, L. Malahova, S. Markov, E. Popova, B. Stojanova, T. Vassilevska, P. Vassilevski: HIFICOMP: Subroutine library for HIghly efFIcient and accurate COMPutations, Program description and User's Guide. CINTI Reg.No.1.A.066.02112-01 13, 1987.

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    Interval Computer Algebra

  36. Popova, E.: WebComputing Service Framework.   Int. Journal Information Theories & Applications 13, 3, 2006, pp. 246-254. (Full Text Reprint - 579K PDF)     WebComputing in action

  37. Popova, E.: Web-Accessible Tools for Interval Linear Systems. Proceedings in Applied Mathematics & Mechanics (PAMM) 5, issue 1, 2005, pp. 713-714. (Abstract, Full Text - 84K PDF)

  38. Popova, E., Ivanova, M.: Scientific Visualization: A Service for Interactive Graphics Generation. Proceedings of the 34th Spring Conference of the Union of Bulgarian Mathematicians, Borovets, April 6-9, 2005, pp. 363-369. (in Bulgarian with English abstract)     Scientific Visualization in action

  39. Popova, E.: Solving Parametric Interval Linear Systems by Mathematica. Mathematics & Education in Mathematics, (Eds. E. Kelevedziev, P. Boyvalenkov), BAS, 2002, 391-396.

  40. Popova, E. D.; Ullrich, C.: Simplification of Symbolic-Numerical Interval Expressions. In O. Gloor (Ed.): Proceedings of the 1998 International Symposium on Symbolic and Algebraic Computation, ACM Press, 1998, pp. 207-214.  (Full Text - 180K PS,  220K PDF)

  41. Popova, E. D.: Mathematica Tools for Explicit Manipulation of Interval Formulas 15th IMACS World Congress on Scientific Computation, Modelling and Applied Mathematics. Volume 2 Numerical Mathematics, 1997, pp. 389-394.

  42. Akyildiz, Y.; Popova, E. D.; Ullrich, C.: Towards a More Complete Interval Arithmetic in Mathematica. Innovation in Mathematics, Proceedings of the Second International Mathematica Symposium, 1997, pp. 29-36.

  43. Popova, E. D.; Ullrich, C.: Directed Interval Arithmetic in Mathematica: Implementation and Applications, Technical Report 96-3, Universitaet Basel, January 1996, pp. 1-44. (Full Text - 570K PDF, 291K PostScript)

  44. Popova, E. D.; Ullrich, C.: Embedding Directed Intervals in Mathematica. Revista de Informatica Teorica e Applicada 3, 2, 1996, pp. 99-115.

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Last updated: February, 2008