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

    General Investigations

  1. Popova, E.D.: Quantified Formulation of an Interval Model in Mechanics, in: I. Georgiev, H. Kostadinov, E. Lilkova (eds.), Advanced Computing in Industrial Mathematics, Studies in Computational Intelligence, 1111, Springer, 2023, pp. 176-187. DOI: 10.1007/978-3-031-42010-8_19 (Preprint)

  2. Popova, E.D.: Proving endpoint dependence in solving interval parametric linear systems. Numerical Algorithms (2021) 86, 3, 1339-1358. DOI: 10.1007/s11075-020-00936-3. Free read-only access: https://rdcu.be/b38aM. (Preprint)

  3. Popova, E.D.: New parameterized solution with application to bounding secondary variables in FE models of structures. Applied Mathematics and Computation (2020) 378, 125205. DOI: 10.1016/j.amc.2020.125205. (Preprint: arxiv:1812.07300)

  4. Popova, E.D.: On a class of parameterized solutions to interval parametric linear systems. C. R. Acad. Bulg. Sci. (2020) 73, 5, 599-611. DOI: 10.7546/CRABS.2020.05.02 free access (Preprint: arxiv:1906.00613)

  5. Popova, E.D., Elishakoff, I.: Novel interval model applied to derived variables in static and structural problems. Archive of Applied Mechanics (2020) 90(4):869-881. DOI: 10.1007/s00419-019-01644-8. Free read-only access: https://rdcu.be/b25i5. (Preprint)

  6. 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 free access.

  7. 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. Free read-only access: https://rdcu.be/bbNCs, (Preprint)

  8. 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. Free read-only access: https://rdcu.be/enuwG, (Preprint)

  9. 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.

  10. 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. Free read-only access: http://rdcu.be/kofz. (Preprint)

  11. 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)

  12. 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. DOI: 10.1007/978-3-319-49544-6_14 (Preprint)

  13. 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. (free access)

  14. 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)

  15. 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)

  16. 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. (Reprint)

  17. Popova, E.D.: On the Unbounded Parametric Tolerable Solution Set, Numerical Algorithms 69(1) (2015), 169-182. DOI: 10.1007/s11075-014-9888-y. Free read-only access: https://rdcu.be/enTEA. (Preprint)

  18. Popova, E.D.: Improved Enclosure for Some Parametric Solution Sets with Linear Shape, Computers and Mathematics with Applications, 68 (2014) 994-1005. DOI: 10.1016/j.camwa.2014.04.005 (free access). Erratum

  19. Popova, E.D.: Inner Estimation of Linear Parametric AE-Solution Sets, Comptes rendus de l'Academie Bulgare des Sciences 67(1) 13-20, 2014. free access: https://buldml.math.bas.bg/en/v/6557

  20. 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. DOI: 10.1080/15502287.2013.8066.

  21. Popova, E.D.: Inner Estimation of the Parametric Tolerable Solution Set, Computers and Mathematics with Applications, 2013, 66(9):1655-1665. DOI: 10.1016/j.camwa.2013.04.007 (free access)

  22. Popova, E.D., M. Hladik: Outer enclosures to the parametric AE solution set, Soft Computing (2013) 17:1403-1414. DOI: 10.1007/s00500-013-1011-0. Free read-only access: https://rdcu.be/enTS9. (Preprint)

  23. J. Garloff, E. D. Popova, and A. P. Smith: Solving Linear Systems with Polynomial Parameter Dependency with Application to the Verified Solution of Problems in Structural Mechanics, in A. Chinchuluun et al. (eds.), Optimization, Simulation, and Control, Springer Optimization and Its Applications 76, 2013, 301–318, Springer Science+Business Media, New York. DOI: 10.1007/978-1-4614-5131-0_19. (Preprint)

  24. 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. DOI: 10.1137/120870359. Preprint 7/2011, IMI-BAS, Sofia, 2011.

  25. Popova, E.D.: The United Solution Set to 3D Linear System with Symmetric Interval Matrix, Proceedings of BGSIAM'11, Demetra, Sofia, 2012, pp. 80-85.

  26. Popova, E.D.: Explicit Description of 2D Parametric Solution Sets, BIT Numerical Mathematics 52(1):179-200, 2012. DOI: 10.1007/s10543-011-0339-z. Free read-only access: https://rdcu.be/enTW7. (Preprint)

  27. 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. free access: http://hdl.handle.net/10525/6558

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

  29. 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)

  30. Anguelov, R., Popova, E.D.: Reliable Simulations for Applied Dynamical Models, in T.E. Simos et al. (Eds), Numerical Analysis and Applied Mathematics, AIP Conf. Proc. 1168, Melville, New York, 2009, pp. 1205-1208. DOI: 10.1063/1.3241284 (Preprint)

  31. 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, 2009.

  32. 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. free access: https://buldml.math.bas.bg/en/v/6560

  33. 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. Free read-only access: https://rdcu.be/enHD3

  34. Popova, E.D. and W. Krämer: Inner and Outer Bounds for Parametric Linear Systems. J. Computational and Applied Mathematics 199 (2007) 2, 310-316. DOI: 10.1016/j.cam.2005.08.048 free access

  35. Popova, E.D.: Computer-Assisted Proofs in Solving Linear Parametric Problems, in the Proceedings of SCAN'06, p. 35, IEEE Computer Society Press, 2006. DOI: 10.1109/SCAN.2006.12. (Preprint - PDF 322K)
    -- Proven monotonicity properties for a benchmark example - (text - PDF, data - ASCII)

  36. 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. DOI: 10.1007/978-3-540-70942-8_41.
    Expanded version in: Preprint No. 3/2005, Institute of Mathematics and Informatics, BAS, Sofia, December 2005, (free access http://hdl.handle.net/10525/3361).

  37. 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)

  38. 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. DOI: 10.1007/11666806_34. (Full Text - PDF 356K)

  39. Popova, E.D.: Generalizing the Parametric Fixed-Point Iteration. Proceedings in Applied Mathematics & Mechanics (PAMM) 4, issue 1, 2004, pp. 680-681. DOI: 10.1002/pamm.200410321 (open archive).

  40. Popova, E.D.: Strong Regularity of Parametric Interval Matrices. Mathematics & Education in Mathematics, 2004, (Eds. I. Dimovski et al.), BAS, pp. 446-451. Free access: SMB, Reprint.

  41. Popova, E.D.: Parametric Interval Linear Solver. Numerical Algorithms 37 (1-4), 2004, 345-356. DOI: 10.1023/B:NUMA.0000049480.57066.fa. Free read-only access: https://rdcu.be/enVgH. (Preprint)

  42. Iankov, R.; Popova, E.D.; Datcheva, M.; Schanz, T.: Modelling a cavity expansion problem under uncertainties. In Proceedings of the University of Rousse, 2004, vol. 41, book 6.1, Mathematics and informatics, Physics, pp. 51–55. (Preprint)

  43. Iankov, R.; Popova, E.D.; Datcheva, M.; Schanz, T.: Numerical Modeling of Consolidation with Uncertainty in Soil Properties. Journal of Theoretical and Applied Mechanics 34(3):43-54, 2004. (free access)

  44. 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. DOI: 10.1007/978-3-540-24588-9_29. (Reprint)

  45. 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)

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

  47. Popova, E.D.: On the Solution of Parametrised Linear Systems. In: W. Krämer, J. Wolff von Gudenberg (Eds.): Scientific Computing, Validated Numerics, Interval Methods. Kluwer Acad. Publishers, 2001, pp. 127-138. (Preprint 200K) DOI: 10.1007/978-1-4757-6484-0_11

  48. Popova, E.D.: Multiplication Distributivity of Proper and Improper Intervals. Reliable Computing 7, 2, 2001, pp.129-140. DOI: 10.1023/A:1011470131086. (Reprint)

  49. Popova, E.D.: All about generalized interval distributive relations. I. Complete proof of the relations, manuscript, Sofia, 2000. English translation of Chapter 2 in Popova, E.D., Generalized Interval Arithmetic - Properties and Implementation, PhD thesis, Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Sofia, 2000.

  50. Popova, E.D.: Algebraic Solutions to a Class of Interval Equations Journal of Universal Computer Science, Vol. 4, No. 1, 1998, pp. 48-67, free access, DOI: 10.3217/jucs-004-01-0048.

  51. 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. (Full Text)

  52. 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. (Full Text - PDF 132K)

    53. Up to the Index

    Interval Interpolation & Approximation

  53. Evgenija D. Popova and Radostin Surilov, Interpolating Vertical Segments, in the Wolfram Demonstrations Project, 2011.

  54. Evgenija D. Popova and Radostin Surilov, Interval Interpolating Polynomial, in the Wolfram Demonstrations Project, 2011.

  55. Markov, S. M.; Popova, E. D.: Interpolation and Estimation using Interval Arithmetic. In: 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. DOI: 10.1007/978-1-4757-9545-5_9 (Reprint)

  56. 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. DOI: 10.1016/0378-4754(95)00110-7. (Full Text - 183K PDF)

  57. 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.

  58. 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.

  59. 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.

  60. 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. DOI: 10.1016/S1474-6670(17)50637-0 free access

  61. 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.

    62. Up to the Index

    Interval Specification & Implementations

  62. 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. Free read-only access: https://rdcu.be/enWoq. (Reprint)

  63. Popova, E. D.: On the Interoperability Between Interval Software. In: Numerical Validation in Current Hardware Architectures, Dagstuhl Seminar Proceedings, vol. 8021, Internationales Begegnungs- und Forschungszentrum fuer Informatik (IBFI), Schloss Dagstuhl, Germany, 2008. DOI: 10.4230/DagSemProc.08021.16 open access with an electronic supplement PDF and a source archive zip)

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

  65. 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)

  66. Popova, E. D., Ullrich, C.: Generalising BIAS Specification Journal of Universal Computer Science, Vol. 3, no. 1, 1997, pp. 23-41 open access, DOI:10.3217/jucs-003-01-0023.

  67. 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. (Full Text)

  68. Popova, E. D.: Interval Operations Involving NaNs Reliable Computing, 2 (2), 1996, pp. 161-165. DOI: 10.1007/BF02425919 (Preprint)

  69. Popova, E. D.: Extended Interval Arithmetic in IEEE Floating-Point Environment. Interval Computations, No 4, 1994, pp. 100-129.

  70. Popova, E. D.: On a Formally Correct Implementation of IEEE Computer Arithmetic Journal of Universal Computer Science, Vol. 1, No. 7, 1995, pp. 560-569 open archive, DOI: 10.3217/jucs-001-07-0560.

  71. 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

  72. 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.

    73. Up to the Index

    Interval Computer Algebra

  73. Popova, E., W. Krämer: Embedding C-XSC Nonlinear Solvers in Mathematica,   Comptes rendus de l'Academie bulgare des Sciences, 64(1):11-20, 2011. free access: https://buldml.math.bas.bg/en/v/6559

  74. 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. DOI: 10.1007/978-3-642-15582-6_56. (Reprint)

  75. E. Popova, W. Krämer, M. Russev: Integration of C-XSC Automatic Differentiation in Mathematica, Preprint No. 3, Institute of Mathematics and Informatics, BAS, 2010. (BulDML source)

  76. E. Popova, 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. DOI: 10.1007/978-3-642-01591-5_7 (Reprint)

  77. Popova, E.: WebComputing Service Framework.   Int. Journal Information Theories & Applications 13, 3, 2006, pp. 246-254. free access

  78. Popova, E.: Web-Accessible Tools for Interval Linear Systems. Proceedings in Applied Mathematics & Mechanics (PAMM) 5, issue 1, 2005, pp. 713-714. DOI: 10.1002/pamm.200510331 (open access)

  79. 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, free access)

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

  81. 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. DOI: 10.1145/281508.281614 free access

  82. 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.

  83. 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. free access ISBN: 1853125059

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

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

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Last updated: January, 2024