Leading Researcher

Nikolaievska Olena Anatoliivna

Candidate (PhD) of Physical and Mathematical Sciences, Senior Researcher

Email: elena_nea@ukr.net, NikolaevskaOA@nas.gov.ua

Biography

Nikolaevska Olena Anatoliivna, born in 1983, has been working at the VM Glushkov Institute of Cybernetics of the National Academy of Sciences of Ukraine since 2008. As a software engineer since May 2008, since November 2008 she has been transferred to the position of junior researcher, as a researcher since 2011, from 2020 to the present she has been transferred to the position of senior researcher .

Specialty by diploma - "Mathematics and Fundamentals of Economics".

In 2010 she successfully defended her dissertation on specialty 01.05.02 - "Mathematical modeling and computational methods".

Scientific bases

Research interests

Least squares problem, weighted least squares problem, weighted pseudo-inverse matrix of Moore-Penrose;
methods and algorithms for solution SLAE with approximate initial data, singular value decomposition of the matrix, weighted singular value decomposition of the matrix;
mathematical models with approximate initial data;
algorithms for solution SLAE for computers with parallel architecture;
programming with multiple precision, GMP, MPFR
machine learning, AI, GPT models

Main results

perturbation theory and error theory for weighted least squares problems are developed;
the errors of the weighted normal pseudoresolution in the case of mismatch of the rank of the original and perturbed matrix are obtained;
an original approach to proving the existence and uniqueness of a normal pseudo-solution in the case of a problem with positively determined weights is proposed;
developed algorithms for solving problems of weighted least squares with positively determined weights with matrices of arbitrary structure and arbitrary rank on computers of MIMD-architecture using arbitrary bit size;
a study of the dependence of the efficiency of algorithms on the decomposition of the original data in solving these problems, as well as on the structure and architecture of MIMD-computers.

Khimich A.N., Nikolaevskaya E.A., Baranov I.A. Weighted least squares perturbation theory. "Matrix Theory - Classics and Advances" edited by Dr. Mykhaylo Andriychuk, 2022, ISBN 978-1-80355-823-3, DOI: https://doi.org/10.5772/intechopen.102885
Nikolaevskaya E.A., Khimich A.N., Chistyakova T.V. Programming with Multiple Precision. - Springer; 1st edition (February 2, 2012)

2026

Oleksandr M. Khimich, Elena A. Nikolaevskaya, Pavlo S.Yershov Development of a Virtual Travel Assistant using the GPTModel. A Springer book series: Smart Innovation,Systems and Technologies. ICT for Intelligent SystemsProceedings of ICTIS 2025, Volume 14, 2026, pp 87–101 DOI: 10.1007/978-981-95-1361-1_7
Khimich, O., Popov, O., Nikolaevskaya, E., Sydoruk, V. Solving Eigenvalue Problems for Skyscraper and Bordered Block-Diagonal Matrices, Numerische Mathematik, 2026
Khimich, O., Popov, O., Nikolaevskaya, E., Sydoruk, V. Development of adaptive algorithms for determining mathematical properties of SLAE and AEP problems based on multi-precision arithmetic, Numerical Linear Algebra with Applications, 2026

2025

Oleksandr M. Khimich, Oleksandr V. Popov, Tamara V. Chistyakova, Elena A. Nikolaevskaya, Pavlo S. Yershov, AI-based Intelligent System for Applied problems: conception and architecture. 2025 IEEE 8th International Conference on Methods and Systems of Navigation and Motion Control (MSNMC) October 21-24, 2025, Kyiv, Ukraine
Oleksandr M. Khimich, Oleksandr V. Popov, Tamara V. Chistyakova, Elena A. Nikolaevskaya, Pavlo S. Yershov, AI-based Intelligent System for Applied problems: Model Generation Web Application Architecture. ProfIT AI 2025: 5th International Workshop of IT-professionals on Artificial Intelligence (ProfIT AI 2025), October 15-17, 2025, Liverpool, UK. Vol-4164 p 250-261
Sydoruk V., Chystiakov O., Benner P., Nikolaievska O. Solving Linear Systems of Equations with Block Skyscraper Structure. Cybernetics and Computer Technologies. 2025. 3. P. 68–78. https://doi.org/10.34229/2707-451X.25.3.6 http://cctech.org.ua/images/docs/Articles/2025/paper_25_3_6.pdf
Oleksandr Khimich, Oleksandr Popov, Elena Nikolaevskaya, Volodymyr SydorukSolving incorrect problems in conditions of approximate data with singular matrices. CompCom 2025, Lecture Notes in Networks and Systems 1425, pp. 1–15, 2025. https://doi.org/10.1007/978-3-031-92608-2_21
Zahorodniy, A. H., Khimich, O. M., Andon, P. I., Dubrovinа, L. A., Radchenko, A. I., Zhuk, O. M., Didenko, Yu. V., Svistunov, S. Ya., Shadura, V. M., Tulchynskyi, V. H., Horbachuk, V. M., Nikolaevska, O. A., Kolomiiets, O. V., Haragulia, S. S., Symonenko, T. V., Zaika, V. M., Novytskyi, O. V., Proskudina, H. Yu., Reznichenko, V. A., Kapitsa, Yu. M., Chernovska, S. M., & Shakhbazyan, K. S. (2025). Implementation of European principles of open science in the National Academy of Sciences of Ukraine. Visnik Nacional Noi Academii Nauk Ukrai Ni, (1), 11–33. https://doi.org/10.15407/visn2025.01.011

2024

Oleksandr M. Khimich, Serhii V. Yershov, Elena A. Nikolaevskaya, Pavlo S. Yershov Development of an Intelligent Search System using GPT model for GrantsForScience platform. ProfIT AI 2024: 4th International Workshop of IT-professionals on Artificial Intelligence (ProfIT AI 2024), September 25–27,2024, Cambridge, MA, USA. Vol-3777. P. 111-119. + Video

2023

Khimich O., Nikolaevska O., & Baranov I. (2023). Features of the use of multi-digit arithmetic in mathematical modeling. PHYSICO-MATHEMATICAL MODELING AND INFORMATION TECHNOLOGIES, (37), 143-148.
DOI: https://doi.org/10.15407/10.15407/fmmit2023.37.143
URL: http://www.fmmit.lviv.ua/index.php/fmmit/article/view/322

2020

Khimich A.N., Nikolaevskaya E.A. Existence and uniqueness of weighted normal pseudosolution // Cybernetics and Systems Analysis, 2020, Vol. 56, No. 4, pp. 28-34.
Khimich A.N., Nikolaevskaya E.A. Existence and Uniqueness of Weighted Normal Pseudosolutions. Cybern Syst Anal 56, 544–549 (2020).
DOI: https://doi.org/10.1007/s10559-020-00270-5
URL: http://www.kibernetika.org/volumes/2020/numbers/04/articles/03/ArticleDetailsUA.html

2017

Khimich O.M., Nikolaevska O.A., Chistyakova T.V. On some methods to improve the accuracy of computer calculations // Mathematical and Computer Modeling. Series: Physical and Mathematical Sciences. Collection of scientific works / V.M. Glushkov Institute of Cybernetics of the NAS of Ukraine, Kamianets-Podilskyi National University named after I. Ohienko, 2017, issue 15, pp. 249–254.
DOI: https: // doi.org/10.32626/2308-5878.2017-15.249-254
URL: http://mcm-math.kpnu.edu.ua/article/view/111630

2016

Khimich O.M., Nikolaevska O.A., Chistyakova T.V. On the algorithm of the least squares method for solving linear systems on hybrid computers // Computer Mathematics, 2016, No. 2, pp. 120−128.
URL: http://dspace.nbuv.gov.ua/handle/123456789/168425

2009

Nikolaevskaya E.A., Khimich A.N., Yakovlev M.F. Solution of the weighted least squares problem with a symmetric positive semi-definite matrix // Computer Mathematics. – 2009. – No. 3. – pp. 36 – 45.
Nikolaevskaya E.A., Chistyakova T.V. Program-algorithmic methods to improve the accuracy of computer solutions // Cybernetics and Systems Analysis. – 2009. – No. 6. – pp. 172 – 176.
Nikolaevskaya E.A., Chistyakova T.V., Program-algorithmic methods to improve the accuracy of computer solutions Cybernetics and Systems Analysis (2009) 45(6) 1004-1007
DOI: 10.1007/s10559-009-9164-7
Nikolaevskaya E.A., Khimich A.N. Error estimation of weighted normal pseudosolution with positive definite weights // Journal of Computational Mathematics and Mathematical Physics. – 2009. – Vol. 49, No. 3. – pp. 422 – 430.
Khimich A.N., Nikolaevskaya E.A., Error estimation for a weighted minimum-norm least squares solution with positive definite weights // Computational Mathematics and Mathematical Physics (2009) 49(3) 409-417
DOI: 10.1134/S0965542509030038

2008

Khimich A.N., Nikolaevskaya E.A. Solution of the weighted least squares problem with approximately given initial data // Collection of scientific works. Theory of optimal solutions. Kyiv: V.M. Glushkov Institute of Cybernetics of the NAS of Ukraine. – 2008. – No. 7. – pp. 132 – 139.
Khimich A.N., Nikolaevskaya E.A. Analysis of the reliability of computer solutions of systems of linear algebraic equations with approximately given initial data // Cybernetics and Systems Analysis.– 2008. – No. 6. – pp. 83 – 95.
Khimich A.N., Nikolaevskaya E.A. Reliability analysis of computer solutions of systems of linear algebraic equations with approximate initial data Cybernetics and Systems Analysis (2008) 44(6) 863-874
DOI: 10.1007/s10559-008-9062-4

2007

Khimich A.N., Nikolaevskaya E.A. Perturbation analysis of the solution of the weighted least squares problem. // Collection of scientific works. Theory of optimal solutions. Kyiv: V.M. Glushkov Institute of Cybernetics of the NAS of Ukraine. – 2007. – No. 6. – pp. 12 – 18.

2006

Khimich A.N., Nikolaevskaya E.A. Error estimation of the solution of the weighted least squares problem // Collection of scientific works. Computer Mathematics. Kyiv: V.M. Glushkov Institute of Cybernetics of the NAS of Ukraine. – 2006. – No. 3. – pp. 36 – 45.

2008

Computer program “Intelligent software tool Inpartool for research and solving computational mathematics problems with approximately given input data” / Khimich O.M., Molchanov I.M., Popov O.V., Chistyakova T.V., Yakovlev M.F., Gerasimova T.O., Zubatenko V.S., Gromovsky O.V., Nesterenko A.N., Polyanko V.V., Rudich O.V., Nikolaevska O.A. – No. 23462; published 17.01.2008.

2009

Computer program “Set of programs for solving the weighted least squares problem with approximately given input data” / Khimich O.M., Nikolaevska O.A. – No. 28880; published 25.05.2009.

2015

Library of intelligent programs for research and solving computational mathematics problems for hybrid computers / Baranov A.Yu., Baranov I.A., Gerasimova T.A. et al. (12 authors) Certificate of copyright registration No. 58055 dated 15.01.2015.
Intelligent software tool Inpartool_G for automatic research and solving linear systems on hybrid computers / Baranov A.Yu., Baranov I.A., Gerasimova T.A. et al. (12 authors) Certificate of copyright registration
No. 58054 dated 15.01.2015.

2018

Certificate of copyright registration with the State Intellectual Property Service of Ukraine: Computer program “Parallel program GausSolver for research and solving linear systems with dense non-singular matrices of arbitrary precision on MIMD computers.” Khimich O.M., Baranov I.A., Nikolaevska O.A., Polyanko V.V., Chistyakova T.V., No. 76941, registration date 19.02.2018.
Certificate of copyright registration with the State Intellectual Property Service of Ukraine: Computer program “Parallel program Slae_svd_mpf_p for research and solving linear systems with dense singular matrices of arbitrary precision” Khimich O.M., Baranov I.A., Nikolaevska O.A., Chistyakova T.V., No. 76942, registration date 19.02.2018.

2019

Certificate of copyright registration: Computer program “Library of intelligent programs for research and solving computational mathematics problems with approximate data on multicore computers with Intel Xeon Phi second generation processors,” Khimich O.M., Baranov I.A., Gerasimova T.O., Nesterenko A.N., Nikolaevska O.A., Polyanko V.V., Popov O.V., Rudich O.V., Sydoruk V.A., Chistyakov O.V., Chistyakova T.V., No. 87589, registration date 09.04.2019.

2021

Certificate of copyright registration, Ukrainian Intellectual Property Institute (Ukrpatent): Computer program “Intelligent computer mathematics system for solving basic problems” (InparSolver). Khimich O.M., Popov O.V., Chistyakova T.V., Sydoruk V.A., Chistyakov O.V., Nesterenko A.N., Baranov I.A., Polyanko V.V., Nikolaevska O.A. (Decision on copyright registration No. 103287 dated 18.03.2021).