Neli Stoyanova Dimitrova
Researcher, Ph D
Birthdate, birthplace:
January 28, 1953; Drenov, region Lovech
Official address:
Bulgarian Academy of Sciences
,
Institute of Mathematics and Informatics
Section "Biomathematics"
Acad. G. Bonchev str., bl. 8
1113 Sofia, Bulgaria
phone: (+3592) 979 21 88
fax: (+3592) 971 36 49
e-mail: nelid@iph.bio.bas.bg
Home address:
Obelya, bl. 121/D/4/72
1387 Sofia, Bulgaria
Education
Degrees
Prior Experience
Fields of Research
Memberships in Professional Organizations
Research projects
Research and Travel Grants
Teaching experience
Publications
Citations
Education:
1972, High-school for German Language in Lovech, Bulgaria
1972-1977 Sofia University
Faculty of Mathematics and Informatics
Master of Science in Mathematical Modelling
Degrees:
Bulgarian Academy of Sciences, Prof. Assistent, 1988
Sofia University, Ph.D. in computational mathematics, 1998
Prior Experience:
1982-1987 Research and Development Laboratory "Programa" Bulgarian Academy of Sciences, Project manager 1988 Division for Mathematical Modelling in Biology,
Center for Biology at the Bulgarian Academy of Sciences
Professor Assistent 1989-1996 Section "Mathematical Modelling in Biology''
Institute of Biophysics
Bulgarian Academy of Sciences
Professor Assistent since 1996 Section "Biomathematics",
Institute of Mathematics and Informatics
Bulgarian Academy of Sciences
Professor Assistent
Fields of Research:
Computer oriented numerical analysis, Interval analysis, Biomathematics
Memberships in Professional Organizations:
International Association for Mathematics and Computers in Simulation (IMACS)
European Society for Mathematical and Theoretical Biology (ESMTB), 1996
Union of Mathematicians in Bulgaria (since 1998)
Research projects:
"Numerical Algorithms with Result Verification'' with the Institute for Numerical Mathematics at the Technical University Vienna, Austria, 1988-1991.
This project presents a first stage in developing algorithms with result verification for polynomial and nonlinear equations, interpolation and approximation problems involving uncertainties, initial value problems for ODE etc. The results are based on nonstandard interval arithmetic, calculus for interval valued functions.
"Mathematical Modelling of Dynamical Processes", IIASA, Laxenburg, Austria, 1990-1993.
The aim of this project was the development of modern methods for mathematical modelling under uncertain data like reliable computing, interval analysis, numerical methods with result verification, controlability of dynamical systems etc. The program system MODYNA was developed as a demonstrative package based on Pascal-SC and Turbo-Pascal involving suitable visualization facilities. MODYNA includes verification algorithms for solving the following mathematical problems: verified computation of matrix exponential, interpolation and least square approximation under interval data, finding zeroes of polynomials, enclosing real roots of nonlinear equations, solving the two point boundary balue problem and the boundary value problem for parabolic PDE etc.
"Implementation of Decimal Floating-point Arithemtic in C according to IEEE Std. 854", Institute for Applied Mathematics at the University Karlsruhe, Germany, 1990-1992.
The purpose of this project was the studying of the newest IEEE Standard 854 for basic computer arithmetic operations and algorithms for their implementation with maximum accuracy. Algorithms for computation of standard function with maximum accuracy were also studied. Programs in C realizing basic operations (addition, subraction, multiplication and division) in decimal floating-point arithmetic were developed.
"Embedding of Verification Algorithms in Computer Algebra Systems", Institute for Informatics, University of Basel, Switzerland, 1995-1996.
It is known that computer algebra systems provide comfortable computational tools for solving mathematical problems: symbolic calculation, exact rational arithmetic, floating-point arithmetic of arbitrary precision. But using rational arithmetic may cause in many applications exponential growth of computational time and storage. The fast way of doing computations is the floating-point arithmetic. In Maple, no attempt is made to keep the result exact or to study the effect of rounding errors or of data uncertainties. In the frames of this project an algorithm with result verification for solving linear systems with intervals in the matrix and in the right-hand side vector is implemented in Maple. The numerical experiments confirm the feasibility of such kind of algorithms even in computer algebra systems.
Research projects within the Bulgarian National Science Fund:
- MM 10/91: "Numerical Methods with Result Verification", 1991-1994;
- MM 521/95: "Numerical Analysis for Problems Involving Uncertain Data", 1995-1998.
These two projects present two stages in developing verification algorithms for solving linear and nonlinear problems involving uncertainties in the data. Theoretical studies in the field of quasilinear spaces of intervals, interval analysis etc. support the construction of the algorithms.
Research and Travel Grants:
Research grants to: Institute for Numerical Mathematics at the Technical University Vienna, Austria, 1989 and 1990, 2 weeks; Institute for Applied Mathematics at the University Karlsruhe, Germany, 1991, 1 month; Institute for Informatics at the University of Basel, Switzerland, 1995, 2 weeks.
Travel grants to: International Conferences SCAN-89 (Basel, Switzerland), SCAN-91 (Oldenburg, Germany) , SCAN-93 (Vienna, Austria), SCAN-95 (Wuppertal, Germany), SCAN-98 (Budapest, Hungary), INTERVAL-96 (Wuerzburg, Germany), ECMBM-96 (Heidelberg, Germany).
Teaching experience:
Lecture course "Numerical Methods for Global Optimization" at the Sofia University, Faculty for Mathematics and Informatics, 1994/95 and 1997/98;
Practical Exercises:
- at the Sofia University, Faculty for Mathematics and Informatics: "Computer Arithmetic and Applications", 1993/94; "Interval Analysis", 1992/93.
- at the Technical University Sofia: Mathematical Analysis, Linear Algebra, Analytical Geometry, Numerical Methods, 1987-1990.
P U B L I C A T I O N S
N. Dimitrova: Ueber die Distributivgesetzte der erweiterten Intervallarithmetik. Computing 24, 1980, 33-49.
N. S. Dimitrova: On an Interval Method for Solving Nonlinear Systems. Computer Arithmetic and Enclosure Methods, L. Atanassova, J. Herzberger (eds.), Elsevier Science Publ., 1992, 215-223.
N. S. Dimitrova: On Some Properties of an Interval Newton Type Method and its Modification. Computing, Suppl. 9, 1993, 21-33.
N. S. Dimitrova: On a Parallel Method for Enclosing Real Roots of Nonlinear Equations. Numerical Methods and Applications, I.T. Dimov, Bl. Sendov, P. S. Vassilevski (Eds.), World Scientific, Singapore, 1994, 78-84.
N. S. Dimitrova: Optimal Solutions of Linear Tridiagonal Systems of Equations Involving Inexact Right-Hand Side. Mathematica Balkanica, Vol. 8, Fasc. 2-3, 1994, 113-130.
N. S. Dimitrova: On a Cubically Convergent Interval Method for Nonlinear Equations. Mathematics and Education in Mathematics, Publ. House of the Bulg. Acad. Sci., Sofia, 1995, 177-188.
N. S. Dimitrova: On a Numerical Approach for Solving a Class of Nonlinear Systems. Scientific Computing and Validated Numerics, G. Alefeld, A. Frommer, B. Lang (Eds.), Akademie Verlag, Berlin, 1996, 147-153.
N. S. Dimitrova: Extending Maple by Verification Routines for Nonlinear Systems. Proc. of 15th IMACS World Congress on Sci. Computation, Modelling and Appl. Math., Numerical Mathematics, Vol.2, A. Sydow (ed.), Wissenschaft & Technik Verlag, Berlin, 1998, 383-388.
N. Dimitrova: On an Approach for Construction of Verification Algorithms for Nonlinear Equations. Mathematics and Education in Mathematics, Publ. House of the Bulg. Acad. Sci., Sofia, 1998, 106-112.
N. S. Dimitrova: On a Verification Algorithm for Tridiagonal Circulant Symmetric Linear Systems. Accepted for publ. in the Proc. of NMA'98 Conf., North Holland, 1999.
N. Dimitrova, S. M. Markov: Distributive Laws in the Extended Interval Arithmetic. Ann. Univ. Sofia, Math. Fac., 71, Part I, 1976/77, 169-185 (in Bulgarian).
N. Dimitrova, S. Markov: Ueber die intervallarithmetische Berechnung des Wertebereichs einer Funktion mit Anwendungen. Freiburger Intervall-Berichte 81/4, Univ. Freiburg, Germany, 1981, 1-22.
N. Dimitrova, S. M. Markov: Interval Methods of Newton Type for Nonlinear Equations. Pliska stud. math. bulg. 5, 1983, 105-117.
N. Dimitrova, S. Markov: Interval-arithmetic Algorithms for Simultaneous Computation of all Polynomial Zeroes. Contributions to Computer Arithmetic and Self-Validating Numerical Methods, C. P. Ullrich (Ed.), IMACS Annals on Computing and Applied Mathematics, J. C. Baltzer Publ., Basel, 7, 1990, 291-300.
N. Dimitrova, S. Markov: On the Interval-arithmetic Presentation of the Range of a Class of Monotone Functions of Many Variables. Computer Aritmetic, Scientific Computation and Mathematical Modelling, E. Kaucher, S. M. Markov, G. Mayer (Eds.), J. C. Baltzer Publ. IMACS, 12, 1991, 213-228.
N. S. Dimitrova, S. M. Markov, E. D. Popova: Extended Interval Arithmetik: New Results and Applications. Computer Arithmetic and Enclosure Methods, L. Atanassova, J. Herzberger (eds.), Elsevier Science Publ., 1992, 225-234.
N. S. Dimitrova, S. M. Markov: On Validated Newton Type Method for Nonlinear Equations. Interval Computations, 2, 1994, 27-51.
N. S. Dimitrova, Ch. P. Ullrich: Implementation of an Algorithm with Result Verification for Linear Systems in Maple. Technical Report 96-2, Universit\"{a}tsrechenzentrum und Institut f\"{u}r Informatik, Universit\"{a}t Basel, Switzerland, January 1996.
N. S. Dimitrova, Ch. P. Ullrich: Verified Solving of Linear Systems with Uncertainties in Maple. Numerical Analysis and its Applications, L. Vulkov, J. Wa\'{s}niewski, P. Yalamov (eds.), Lecture Notes in Computer Science, vol. 1196, Springer, 1997, 142-149.
N. Dimitrova, P. Zlateva: Investigation of the Methane Fermentation Process Using Interval Analysis. Automatica \& Informatics, 5-6, 1994, 120-123 (in Bulgarian).
N. Dimitrova, P. Zlateva: Study of the Steady-States of Methane Fermentation under Uncertain Data. Lecture Notes on Biomathematics and Bioinformatics'95, M. Candev (Ed.), DATECS Publ., Sofia, 1995, 90-99.
S. Markov, N. Dimitrova: Rechengesetze der erweiterten Intervallarithmetik. Freiburger Intervall-Berichte 79/10, Universit\"{a}t Freiburg, 1979, 1-20.
N. Dimitrova, S. Markov: Verified Computation of Fast Decreasing Polynomials. Reliable Computing, 5, 3, 1999, 229-240.
M. Krastanov, N. Dimitrova: On a Stabilizing Control Design for a Methane Fermentation Process. Mathematics and Education in Mathematics, Proc. of 28th Spring Conf. of UBM, 1999, 192-198.
M. Krastanov, N. Dimitrova: Feedback Control of an Anaerobic Fermentation Process Under Uncertain Data. Mathematics and Education in Mathematics, Proc. of 29th Spring Conf. of UBM, 2000, 184-191.
N. Dimitrova, I. Simeonov: Steady States Analysis of an Anaerobic Biotechnological Process Under Uncertainties. Submitted Mathematical Biosciences.
S. Markov, N. Dimitrova: Mathematical Models of Biochemical processes in Living Organisms. Submitted to Biosystems.
Citations
Yu. Shokin: Interval Analysis. Nauka, Novosibirsk, 1981 (in Russian).
Publication No. 22 is cited
A. S. Kalmykov, Yu. Shokin, S. Yuldashev: Methods of Interval Analysis. Nauka, Novosibirsk, 1986 (in Russian).
Publications No. 1, 11, 13 are cited
K. Nickel: Optimiation Using Interval Mathematics. Freiburger Intervall-Berichte 86/7, Univ. Freiburg, Germany, 1986, 55-83.
Publication No. 12 is cited
E. V. Levner, A. S. Ptuskin: A Fuzzy Interval Method for Scheduling Transportation Robots. Mathematical Modelling and Scientific Computing, A.S. Andreev, S.M. Markov, Ch. Ullrich (eds.), Bulg. Acad. Sci., Sofia, 1991.
Publication No. 15 is cited
V. M. Nesterov: How to use monotonicity-type information to get better estimates of the range of real-valued functions. Interval Computations 4, 1993, 3-12.
Publications No. 12 and 15 are cited %No. 12: N. Dimitrova, S. M. Markov. \"{U}ber die %intervall-arithmetische Berechnung des Wertebereichs einer %Funktion mit Anwendungen, Freiburger Intervall-Berichte, Univ. %Freiburg, 81/4 (1981), 1-22.
Andreev A., Kjurkchiev N., Two-sided methods for solving equations. Contributions to Computer Arithmetic and Self-Validating Numerical Methods (Ed. C. P. Ullrich), IMACS Annals on computing and applied mathematics, vol. 7, 1990, J. C. Baltzer A. G. Publ. Co., Basel, Switzerland, 133-147.
Publication No. 14 is cited
Markov, S. M.: Extended interval arithmetic involving infinite intervals. Mathematica Balkanica, New Series, {\sl 6}, 3, 269-304 (1992).
Publication No. 1 is cited
Markov, S. M.: On the Presentation of Ranges of Monotone Functions using Interval Arithmetic. Interval Computations, No 4(6), 1992, 19-31.
Publication No. 1 is cited
Markov S., On two interval-algebraic structures, Ann. Univ. de Sofia, Fac. Math. Inform., 89, livre 1 (Mathematics), 1995, 129-164 (in Bulgarian)
Publications No. 1 is cited
N. Glazunov: On some algebraic structures of interval analysis and their extensions. In: S. Markov (Ed.): Scientific Computation and Mathematical Modelling. DATECS Publ., Sofia, 1993, 11-12.
Publication No. 16 is cited
V. Nesterov, Interval and twin arithmetics. Volume of extended abstracts INTERVAL'96, 30.09-2.10.1996, Wuerzburg, 89-90.
Publication No. 16 is cited
Last updated: 22.08.2000
