This article is cited in 15 papers

Iterative gradient descent methods for solving linear equations

A. B. Samokhin^a, A. S. Samokhina^b, A. Ya. Sklyar^a, Yu. V. Shestopalov<sup>a

a</sup> Russian Technological University MIREA, Moscow, 119454 Russia
^b Institute of Control Sciences, Russian Academy of Sciences, Moscow, 117997 Russia

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.

UDC: 541.11

Received: 23.03.2018
Revised: 30.03.2019
Accepted: 10.04.2019

DOI: 10.1134/S0044466919080143

 English version: Computational Mathematics and Mathematical Physics, 2019, 59:8, 1267–1274

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