Vestnik KRAUNC. Fiz.-Mat. Nauki. 2022. vol. 40. no. 3. pp. 153–164. ISSN 2079-6641

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MSC 68T07

Research Article

Approaches to solving systems of linear algebraic equations using neural networks

V. A. Galkin¹², T. V. Gavrilenko¹², A. D. Smorodinov¹²

¹Surgut Branch of SRISA 628426, Surgut, Energetikov st., 4, Russia
²Surgut State University, 628412, Surgut, Lenina st., 1, Russia

System linear is the main solution for an essential class of mathematical modeling problems. The study of the possibility of solving system linear using neural networks will allow creating new approaches to solving problems of mathematical modeling. A new way of solving systems of linear equations using neural networks is presented.
Feedforward networks and a stochastic gradient descent algorithm are used. The stages of designing a neural network are described, as well as the process of choosing the optimal NN structure, based on the computational experiments performed. The results of using neural networks for solving systems of linear equations are presented. The expediency of using NN for problems of this type is substantiated.

Key words: systems of linear algebraic equations, Neural networks, gradient descent

DOI: 10.26117/2079-6641-2022-40-3-153-164

Original article submitted: 03.10.2022

Revision submitted: 25.11.2022

For citation. Galkin V. A., Gavrilenko T. V., Smorodinov A. D. Approaches to solving systems of linear algebraic equations using neural networks. Vestnik KRAUNC. Fiz.-mat. nauki. 2022, 40: 3, 153-164. DOI: 10.26117/2079-6641-2022-40-3-153-164

Competing interests. The authors declare that there are no conflicts of interest regarding authorship and publication.

Contribution and Responsibility. All authors contributed to this article. Authors are solely responsible for providing the final version of the article in print. The final version of the manuscript was approved by all authors.

Funding. The publication was made within the framework of the state task of the Federal State Institution FNTs NIISI RAS (Performance of fundamental scientific research GP 47) on topic No. 0580-2021-0007 «Development of methods for mathematical modeling of distributed systems and corresponding calculation methods»

The content is published under the terms of the Creative Commons Attribution 4.0 International License (

© Galkin V. A., Gavrilenko T. V., Smorodinov A. D., 2022


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Galkin Valery Alekseevich – D. Sci. (Phys. & Math.), Professor, Surgut State University; Director, Branch of SRISA, Surgut, Russia, ORCID 0000-0002-9721-4026.

Gavrilenko Taras Vladimirovich – PhD (Tech.), docent, Surgut State University; Deputy Director, Branch of SRISA, Surgut, Russia, ORCID 0000-0002-3243-2751.

Smorodinov Aleksandr Denisovich – Postgraduate Student of the Department of Applied Mathematics, Lecturer of the Department of ASOIU, Surgut State University; Engineer of the Department of Biophysics and Neurocybernetics, Branch of SRISA, Surgut, Russia, ORCID 0000-0002-9324-1844.