Geodesic
Approaches to solving systems of linear algebraic equations using neural networks
Vestnik KRAUNC. Fiziko-matematičeskie nauki, Tome 40 (2022) no. 3, pp. 153-164

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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.
Keywords: systems of linear algebraic equations, Neural networks
Mots-clés : gradient descent. 
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     author = {V. A. Galkin and T. V. Gavrilenko and A. D. Smorodinov},
     title = {Approaches to solving systems of linear algebraic equations using neural networks},
     journal = {Vestnik KRAUNC. Fiziko-matemati\v{c}eskie nauki},
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     publisher = {mathdoc},
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     number = {3},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VKAM_2022_40_3_a12/}
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V. A. Galkin; T. V. Gavrilenko; A. D. Smorodinov. Approaches to solving systems of linear algebraic equations using neural networks. Vestnik KRAUNC. Fiziko-matematičeskie nauki, Tome 40 (2022) no. 3, pp. 153-164. http://geodesic.mathdoc.fr/item/VKAM_2022_40_3_a12/