Iterative Gradient Descent Methods for Solving Linear Equations

被引：10
|
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
收藏
页码：1267 / 1274
页数：8
相关论文
共 50 条
  • [31] Iterative methods for solving linear systems of equations on FPGA-based machines
    Xu, XZ
    Ziavras, SG
    COMPUTERS AND THEIR APPLICATIONS, 2003, : 472 - 475
  • [32] ITERATIVE METHOD FOR SOLVING PARTITIONED LINEAR EQUATIONS
    KYDES, AS
    TEWARSON, RP
    COMPUTING, 1975, 15 (04) : 357 - 363
  • [33] An iterative algorithm for solving sparse linear equations
    Walker, Stephen G.
    COMMUNICATIONS IN STATISTICS-SIMULATION AND COMPUTATION, 2017, 46 (07) : 5113 - 5122
  • [34] Iterative Method for Solving a System of Linear Equations
    Kryshchuk, Mykola
    Lavendels, Jurijs
    ICTE 2016, 2017, 104 : 133 - 137
  • [35] Improved Gradient Descent Iterations for Solving Systems of Nonlinear Equations
    Stanimirovic, Predrag S. S.
    Shaini, Bilall I. I.
    Sabi'u, Jamilu
    Shah, Abdullah
    Petrovic, Milena J. J.
    Ivanov, Branislav
    Cao, Xinwei
    Stupina, Alena
    Li, Shuai
    ALGORITHMS, 2023, 16 (02)
  • [36] Gradient-based maximal convergence rate iterative method for solving linear matrix equations
    Zhou, Bin
    Lam, James
    Duan, Guang-Ren
    INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS, 2010, 87 (03) : 515 - 527
  • [37] Iterative methods for solving absolute value equations
    Ali, Rashid
    Ali, Asad
    Iqbal, Shahid
    JOURNAL OF MATHEMATICS AND COMPUTER SCIENCE-JMCS, 2022, 26 (04): : 322 - 329
  • [38] NEW ITERATIVE METHODS FOR SOLVING INTEGRAL EQUATIONS
    Noor, Muhammad Aslam
    Noor, Khalida Inayat
    Al-Said, Eisa
    INTERNATIONAL JOURNAL OF MODERN PHYSICS B, 2011, 25 (32): : 4655 - 4660
  • [39] ITERATIVE METHODS FOR SOLVING INTEGRAL-EQUATIONS
    KLEINMAN, RE
    VANDENBERG, PM
    RADIO SCIENCE, 1991, 26 (01) : 175 - 181
  • [40] On iterative methods for solving equations with covering mappings
    Zhukovskaya T.V.
    Zhukovskii E.S.
    Numerical Analysis and Applications, 2016, 9 (4) : 277 - 287
12345