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



General Investigations

  1. Popova, E.D.: Algebraic solution to interval equilibrium equations of truss structures. Applied Mathematical Modelling 65 (2019) 489-506. DOI: 10.1016/j.apm.2018.08.021 (Preprint)

  2. Popova, E.D.: Rank one interval enclosure of the parametric united solution set. BIT Numerical Mathematics 59 (2) 2019, 503–521. DOI: 10.1007/s10543-018-0739-4 For a free full-text view-only access click here. (Preprint)

  3. Popova, E.D.: Equilibrium equations in interval models of structures. Int. J. Reliability and Safety 12 (1/2) 2018, 218-235. DOI: 10.1504/IJRS.2018.10013814

  4. Popova, E.D.: Enclosing the solution set of parametric interval matrix equation A(p)X = B(p), Numerical Algorithms 78(2):423-447, 2018. DOI: 10.1007/s11075-017-0382-1. (Preprint)

  5. Popova, E.D.: Parameterized Outer Estimation of AE-Solution Sets to Parametric Interval Linear Systems, Applied Mathematics and Computation 311 (2017) 353–360. DOI: 10.1016/j.amc.2017.05.042. (Preprint)

  6. Popova, E.D.: Improved solution to the generalized Galilei’s problem with interval loads, Archive of Applied Mechanics 87 (2017) (1):115-127. DOI: 10.1007/s00419-016-1180-2. For a free full-text view-only access click here. (Preprint)

  7. Popova, E.D.: Interval Model of Equilibrium Equations in Mechanics, in: Freitag, S., Muhanna, R. L., Mullen, R. L. (eds.) Proceedings of REC’2016, Ruhr University Bochum, pp. 241–255, 2016.

  8. Popova, E.D.: Interval Algebraic Approach to Equilibrium Equations in Mechanics, in: K. Georgiev, M. Todorov, I. Georgiev (eds.), Advanced Computing in Industrial Mathematics, Studies in Computational Intelligence 681, Springer, 2017, pp. 161-173. (Preprint; The final publication is available at Springer via DOI: 10.1007/978-3-319-49544-6_14)

  9. Popova, E.D.: Outer bounds for the parametric controllable solution set with linear shape,in M. Nehmeier et al. (Eds.): SCAN 2014, LNCS 9553, pp. 138–147, 2016. DOI: 10.1007/978-3-319-31769-4_12 (Preprint)

  10. Hladik, M., Popova, E.D.: Maximal inner boxes in parametric AE-solution sets with linear shape, Applied Mathematics and Computation 270 (2015) 606-619. DOI: 10.1016/j.amc.2015.08.003 (Preprint)

  11. Popova, E.D.: Solvability of Parametric Interval Linear Systems of Equations and Inequalities, SIAM Journal on Matrix Analysis and Applications 36 (2015) 615-633. DOI: 10.1137/140966459

  12. Popova, E.D.: On the Unbounded Parametric Tolerable Solution Set, Numerical Algorithms 69(1) (2015), 169-182. (http://dx.doi.org/10.1007/s11075-014-9888-y) (Preprint)

  13. Popova, E.D.: Improved Enclosure for Some Parametric Solution Sets with Linear Shape, Computers and Mathematics with Applications, 68 (2014) 994-1005. Erratum, (Preprint)

  14. Popova, E.D.: Inner Estimation of Linear Parametric AE-Solution Sets, Comptes rendus de l'Academie Bulgare des Sciences 67(1) 13-20, 2014.

  15. Popova, E.D.: On ``Overestimation-free Computational Version of Interval Analysis [Int. J. Comput. Meth. Eng. Sci. Mech. 13 (2012) 319-328]", Int. J. Comput. Meth. Eng. Sci. Mech., 2013, 14(6):491-494.(http://dx.doi.org/10.1080/15502287.2013.806606)

  16. Popova, E.D.: Inner Estimation of the Parametric Tolerable Solution Set, Computers and Mathematics with Applications, 2013, 66(9):1655-1665. http://dx.doi.org/10.1016/j.camwa.2013.04.007 (Preprint)

  17. Popova, E.D., M. Hladik: Outer enclosures to the parametric AE solution set, Soft Computing (2013) 17:1403-1414. http://dx.doi.org/10.1007/s00500-013-1011-0 (Preprint)

  18. Popova, E.D.: Explicit Description of AE Solution Sets for Parametric Linear Systems, SIAM Journal on Matrix Analysis and Applications 33(4), 2012, 1172–1189. http://dx.doi.org/10.1137/120870359 (Preprint)

  19. Popova, E.D.: Explicit Description of 2D Parametric Solution Sets, BIT Numerical Mathematics 52(1):179-200, 2012. http://dx.doi.org/10.1007/s10543-011-0339-z (Preprint)

  20. Popova, E.D., Krämer, W.: Characterization of AE Solution Sets to a Class of Parametric Linear Systems, Comptes rendus de l'Academie bulgare des Sciences 64(3)325-332, 2011.

  21. Popova, E.D.: Explicit Characterization of a Class of Parametric Solution Sets, Comptes rendus de l'Academie bulgare des Sciences, 62(10)1207-1216, 2009.

  22. Popova, E.D., Kolev, L., Krämer, W.: A Solver for Complex-Valued Parametric Linear Systems, Serdica Journal of Computing, 4, 2010, pp. 123–132.

  23. Anguelov, R., Popova, E.D.: Topological structure preserving numerical simulations of dynamical models, Journal of Computational and Applied Mathematics 235 (2010), pp. 358-365. DOI: 10.1016/j.cam.2010.05.038 (open archive)

  24. Anguelov, R., Popova, E.D.: Reliable Simulations for Applied Dynamical Models, in T.E. Simos et al. (Eds), Numerical Analysis and Applied Mathematics, American Inst. of Physics Conference Proceedings 1168, Melville, New York, 2009, pp. 1205-1208.

  25. Garloff, J., Popova, E.D., Smith, A., Solving Linear Systems with Polynomial Parameter Dependency in the Reliable Analysis of Structural Frames, in N. Sims & K. Worden, Eds., Proceedings of the 2nd Int. Conf. on Uncertainty in Structural Dynamics, University of Sheffield, UK, 147-156 (2009). Expanded version: Garloff, J., Popova, E.D., Smith, A.: Solving Linear Systems with Polynomial Parameter Dependency, Preprint No. 1/2009, Institute of Mathematics and Informatics, BAS, Sofia, January 2009. (Full Text - PDF 518K)

  26. Popova, E.D.: Mathematica Connectivity to Interval Libraries filib++ and C-XSC, in: A. Cuyt, W. Krämer, W. Luther, P. Markstein (Eds.), Numerical Validation, Lecture Notes in Computer Science 5492, pp. 117–132, Springer-Verlag Berlin Heidelberg, 2009.

  27. Popova, E.D. and W. Krämer: Visualizing Parametric Solution Sets, BIT Numerical Mathematics 48(1): 95-115, 2008. (DOI:10.1007/s10543-007-0159-3)

  28. Popova, E.D.: Computer-Assisted Proofs in Solving Linear Parametric Problems, in the Proceedings of SCAN'06, p. 35, IEEE Computer Society Press, 2006. (Full Text - PDF 322K)
    -- Proven monotonicity properties for a benchmark example - (text - PDF, data - ASCII)

  29. Popova, E.D., 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)

  30. Popova, E.D.: 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)

  31. Popova, E.D.: 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)

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

  33. Popova, E.D.: 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)

  34. Popova, E.D.: 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)

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

  36. Popova, E.D.; 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)

  37. Popova, E.D.; 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)

  38. 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)

  39. 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)

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

  41. Popova, E.D.: All about generalized interval distributive relations. I. Complete proof of the relations, in Popova, E.D., Generalized Interval Arithmetic - Properties and Implementation, PhD thesis, Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Sofia, 2000.

  42. 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: PostScript, PDF)

  43. 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)

  44. 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

  46. Evgenija D. Popova and Radostin Surilov, Interpolating Vertical Segments, in the Wolfram Demonstrations Project.

  47. Evgenija D. Popova and Radostin Surilov, Interval Interpolating Polynomial, in the Wolfram Demonstrations Project.

  48. 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)

  49. 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.

  50. 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.

  51. 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.

  52. 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.

  53. 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)

  54. 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

  56. M. Zimmer, W. Krämer, E. Popova: Solvers for the Verified Solution of Parametric Linear Systems, Computing, (2012) 94: 109–123. (DOI 10.1007/s00607-011-0170-z)

  57. E. Popova, W. Krämer, M. Russev: Integration of C-XSC Automatic Differentiation in Mathematica, Preprint No.~3, IMI, BAS, 2010.

  58. 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)

  59. 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)

  60. 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)

  61. 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)

  62. 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)

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

  64. 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)

  65. 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)

  66. 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

  67. 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

  69. Popova, E., W. Krämer: Embedding C-XSC Nonlinear Solvers in Mathematica,   Comptes rendus de l'Academie bulgare des Sciences, 64(1), 11-20, 2011.

  70. Popova, E., W. Krämer: Communicating Functional Expressions from Mathematica to C-XSC,   in K. Fukuda, J. van der Hoeven, M. Joswig, N. Takayama (Eds.), Mathematical Software - ICMS'2010, Lecture Notes in Computer Science 6327, Springer-Verlag, 2010, pp. 354-365.

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

  72. 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)

  73. 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

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

  75. 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)

  76. 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.

  77. 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.

  78. 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)

  79. 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: November, 15, 2018