Iterative Gradient Descent Methods for Solving Linear Equations

A. B. Samokhin; A. S. Samokhina; A. Ya. Sklyar; Yu. V. Shestopalov

doi:10.1134/S0965542519080141

Iterative Gradient Descent Methods for Solving Linear Equations

Authors: Samokhin A.B.¹, Samokhina A.S.², Sklyar A.Y.¹, Shestopalov Y.V.¹
Affiliations:
1. Russian Technological University MIREA
2. Institute of Control Sciences, Russian Academy of Sciences
Issue: Vol 59, No 8 (2019)
Pages: 1267-1274
Section: Article
URL: https://journals.rcsi.science/0965-5425/article/view/180736
DOI: https://doi.org/10.1134/S0965542519080141
ID: 180736

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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.