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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2019, Volume 59, Number 8, Pages 1331–1339
DOI: https://doi.org/10.1134/S0044466919080143 (Mi zvmmf10935) 		 
This article is cited in 11 scientific papers (total in 11 papers)

Iterative gradient descent methods for solving linear equations

A. B. Samokhina, A. S. Samokhinab, A. Ya. Sklyara, Yu. V. Shestopalova

a Russian Technological University MIREA, Moscow, 119454 Russia
b Institute of Control Sciences, Russian Academy of Sciences, Moscow, 117997 Russia
Citations (11)
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DOI: https://doi.org/10.1134/S0044466919080143
Abstract: The paper presents the results on the use of gradient descent algorithms for constructing iterative methods for solving linear equations. A mathematically rigorous substantiation of the convergence of iterations to the solution of the equations is given. Numerical results demonstrating the efficiency of the modified iterative gradient descent method are presented.
Key words: systems of linear algebraic equations, gradient descent, iterative methods.
Funding agency Grant number
Ministry of Education and Science of the Russian Federation 2.1361.2017/ПЧ
This work was supported by the Ministry of Education and Science of the Russian Federation, grant no.В 2.1361.2017/PCh.
Received: 23.03.2018
Revised: 30.03.2019
Accepted: 10.04.2019
English version:
Computational Mathematics and Mathematical Physics, 2019, Volume 59, Issue 8, Pages 1267–1274
DOI: https://doi.org/10.1134/S0965542519080141
Bibliographic databases:
Document Type: Article
UDC: 541.11
Language: Russian
Citation: A. B. Samokhin, A. S. Samokhina, A. Ya. Sklyar, Yu. V. Shestopalov, “Iterative gradient descent methods for solving linear equations”, Zh. Vychisl. Mat. Mat. Fiz., 59:8 (2019), 1331–1339; Comput. Math. Math. Phys., 59:8 (2019), 1267–1274
Citation in format AMSBIB
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    • This publication is cited in the following 11 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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