Iterative Gradient Descent Methods for Solving Linear Equations

被引：11

作者：

Samokhin, A. B. ^{[1
]}

Samokhina, A. S. ^{[2
]}

Sklyar, A. Ya ^{[1
]}

Shestopalov, Yu, V ^{[1
]}

机构：

[1] Russian Technol Univ MIREA, Moscow 119454, Russia

[2] Russian Acad Sci, Inst Control Sci, Moscow 117997, Russia

来源：

COMPUTATIONAL MATHEMATICS AND MATHEMATICAL PHYSICS | 2019年 / 59卷 / 08期

关键词：

systems of linear algebraic equations; gradient descent; iterative methods;

D O I：

10.1134/S0965542519080141

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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.

引用

页码：1267 / 1274

页数：8

共 6 条

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[2]

Polyak B. T., 1987, Introduction to optimization

[3]

SAAD Y, 1986, SIAM J SCI STAT COMP, V7, P856, DOI 10.1137/0907058

[4]

Samarskii A. A., 1989, Numerical Methods for Grid Equations

[5]

[Самохин А.Б. Samokhin A.B.], 2012, [Электромагнитные волны и электронные системы, Elektromagnitnye volny i elektronnye sistemy], V17, P28

[6] Stationary iteration methods for solving 3D electromagnetic scattering problems [J].

Samokhin, Alexander ;

Shestopalov, Yury ;

Kobayashi, Kazuya .

APPLIED MATHEMATICS AND COMPUTATION, 2013, 222 :107-122

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