ANALYSIS OF THE TRUNCATED CONJUGATE GRADIENT METHOD FOR LINEAR MATRIX EQUATIONS

被引：3
作者：
Simoncini, Valeria [1 ,2 ,3 ]
Hao, Yue [4 ]
机构：
[1] Alma Mater Studiorum Univ Bologna, Dipartimento Matemat & AM2, Piazza Porta S Donato 5, I-40127 Bologna, Italy
[2] IMATI CNR, Pavia, Italy
[3] IAC CNR, Bari, Italy
[4] Inst Appl Phys & Computat Math, High Performance Comp Ctr, Beijing 100088, Peoples R China
来源：
SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS | 2023年 / 44卷 / 01期
基金：
海南省自然科学基金; 中国国家自然科学基金;
关键词：
conjugate gradients; linear matrix equations; truncation strategies; low-rank methods; KRYLOV SUBSPACE METHODS; LOW-RANK METHODS; LYAPUNOV EQUATIONS; SYSTEMS; LANCZOS;
D O I：
10.1137/22M147880X
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
The matrix-oriented version of the conjugate gradient (CG) method can be used to approximate the solution to certain linear matrix equations. To limit memory consumption, low -rank reduction of the factored iterates is often employed, possibly leading to disruption of the regular convergence behavior. We analyze the properties of the method in the matrix regime and identify the quantities that are responsible for early termination, usually stagnation, when truncation is in effect. Moreover, we illustrate relations between CG and a projection technique directly applied to the same matrix equation.
引用
收藏
页码：359 / 381
页数：23
相关论文
共 50 条
  • [21] A Modified Conjugate Gradient Method for Solving Large-Scale Nonlinear Equations
    Guan, Hongbo
    Wang, Sheng
    [J]. MATHEMATICAL PROBLEMS IN ENGINEERING, 2021, 2021 (2021)
  • [22] An Efficient Conjugate Gradient Method for Convex Constrained Monotone Nonlinear Equations with Applications
    Abubakar, Auwal Bala
    Kumam, Poom
    Mohammad, Hassan
    Awwal, Aliyu Muhammed
    [J]. MATHEMATICS, 2019, 7 (09)
  • [23] DERIVATIVE-FREE RMIL CONJUGATE GRADIENT METHOD FOR CONVEX CONSTRAINED EQUATIONS
    Ibrahim, Abdulkarim Hassan
    Isa, Garba Abor
    Usman, Halima
    Abubakar, Jamilu
    Abubakar, Auwal Bala
    [J]. THAI JOURNAL OF MATHEMATICS, 2020, 18 (01): : 212 - 232
  • [24] The matrix iterative methods for solving a class of generalized coupled Sylvester-conjugate linear matrix equations
    Xie, Ya-Jun
    Ma, Chang-Feng
    [J]. APPLIED MATHEMATICAL MODELLING, 2015, 39 (16) : 4895 - 4908
  • [25] The optimal convergence factor of the gradient based iterative algorithm for linear matrix equations
    Wang, Xiang
    Liao, Dan
    [J]. FILOMAT, 2012, 26 (03) : 607 - 613
  • [26] The deflated conjugate gradient method: Convergence, perturbation and accuracy
    Kahl, K.
    Rittich, H.
    [J]. LINEAR ALGEBRA AND ITS APPLICATIONS, 2017, 515 : 111 - 129
  • [27] A MODIFIED SPECTRAL CONJUGATE GRADIENT PROJECTION METHOD FOR SOLVING NONLINEAR MONOTONE SYMMETRIC EQUATIONS
    Wan, Zhong
    Liu, WeiYi
    Wang, Chang
    [J]. PACIFIC JOURNAL OF OPTIMIZATION, 2016, 12 (03): : 603 - 622
  • [28] Induced Dimension Reduction method for solving linear matrix equations
    Astudillo, Reinaldo
    van Gijzen, Martin B.
    [J]. INTERNATIONAL CONFERENCE ON COMPUTATIONAL SCIENCE 2016 (ICCS 2016), 2016, 80 : 222 - 232
  • [29] Cyclic gradient based iterative algorithm for a class of generalized coupled Sylvester-conjugate matrix equations
    Wang, Wenli
    Qu, Gangrong
    Song, Caiqin
    [J]. JOURNAL OF THE FRANKLIN INSTITUTE-ENGINEERING AND APPLIED MATHEMATICS, 2023, 360 (11): : 7206 - 7229
  • [30] EXPLICITLY PRECONDITIONED CONJUGATE-GRADIENT METHOD FOR THE SOLUTION OF UNSYMMETRIC LINEAR-SYSTEMS
    KAPORIN, IE
    [J]. INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS, 1992, 44 (1-4) : 169 - 187
12345