E.D.Popova
Selected Papers on Interval Mathematics & Computing
General Investigations
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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 here: https://rdcu.be/b38aM.
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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
(Preprint)
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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)
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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
Read and share here: https://rdcu.be/b25i5.
(Preprint)
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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)
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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
Read and share here: https://rdcu.be/bbNCs
(Preprint)
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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
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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)
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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)
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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)
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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.
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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)
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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)
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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)
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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
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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)
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Popova, E.D.: Improved Enclosure for Some Parametric Solution Sets with Linear Shape,
Computers and Mathematics with Applications, 68 (2014)
994-1005.
Erratum,
(Preprint)
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Popova, E.D.: Inner Estimation of Linear Parametric AE-Solution Sets,
Comptes rendus de l'Academie Bulgare des Sciences 67(1)
13-20, 2014.
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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)
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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)
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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)
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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)
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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)
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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.
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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.
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Popova, E.D., Kolev, L., Krämer, W.: A Solver for Complex-Valued Parametric Linear Systems,
Serdica Journal of Computing, 4, 2010, pp.
123–132.
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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)
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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.
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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)
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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.
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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)
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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.
(Full Text - PDF 550K)
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Popova, E.D. and W. Krämer: Inner and Outer Bounds for Parametric Linear Systems.
J. Computational and Applied Mathematics 199 (2007) 2, 310-316.
(Preprint)
DOI: 10.1016/j.cam.2005.08.048
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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)
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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)
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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)
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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)
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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)
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Popova, E.D.: Parametric Interval Linear Solver. Numerical Algorithms 37 (1-4), 2004,
345-356. (Abstract, Full Text - PDF)
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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)
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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)
- 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)
- 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)
- Popova, E.D.: Multiplication Distributivity of Proper and Improper
Intervals. Reliable Computing 7, 2, 2001, pp.129-140.
(Abstract,
Full Text: PostScript, PDF)
- 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.
- 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)
- 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)
- 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)
Interval Interpolation & Approximation
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Evgenija D. Popova and Radostin Surilov, Interpolating Vertical Segments, in
the Wolfram Demonstrations Project.
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Evgenija D. Popova and Radostin Surilov, Interval Interpolating Polynomial, in
the Wolfram Demonstrations Project.
- 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)
- 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.
- 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.
- 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.
- 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.
- 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)
- 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)
Interval Specification & Implementations
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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)
- 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)
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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)
- 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)
- 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)
- 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)
- Popova, E. D.: Interval Operations Involving NaNs Reliable Computing, 2 (2), 1996, pp. 161-165.
(Abstract,
Full Text 27K PostScript)
- 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)
- 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)
- 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
- 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.
Interval Computer Algebra
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Popova, E., W. Krämer: Embedding C-XSC Nonlinear Solvers in
Mathematica,
Comptes rendus de l'Academie bulgare des
Sciences, 64(1),
11-20, 2011.
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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.
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E. Popova, W. Krämer, M. Russev: Integration of C-XSC
Automatic Differentiation in Mathematica,
Preprint
No.~3, IMI, BAS, 2010.
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Popova, E.: WebComputing Service Framework.
Int. Journal Information Theories & Applications 13, 3, 2006,
pp. 246-254.
(Full Text Reprint - 579K PDF)
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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)
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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)
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Popova, E.: Solving Parametric Interval Linear Systems by
Mathematica. Mathematics & Education in Mathematics, (Eds. E. Kelevedziev, P. Boyvalenkov), BAS, 2002, 391-396.
- 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)
- 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.
- 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.
- 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)
- Popova, E. D.; Ullrich, C.: Embedding Directed Intervals in
Mathematica. Revista de Informatica Teorica e Applicada
3, 2, 1996, pp. 99-115.
Last updated: January, 2021