Iterative solution to a class of complex matrix equations and its application in time-varying linear system

被引：7
|
作者：
Wang, Wenli [1 ]
Song, Caiqin [1 ,2 ]
Ji, Shipu [3 ]
机构：
[1] Jinan Univ, Sch Math Sci, Jinan 250022, Peoples R China
[2] Univ Nevada, Dept Math & Stat, Reno, NV 89503 USA
[3] Guizhou Normal Univ, Sch Int Educ, Guiyang 550025, Peoples R China
来源：
JOURNAL OF APPLIED MATHEMATICS AND COMPUTING | 2021年 / 67卷 / 1-2期
基金：
安徽省自然科学基金;
关键词：
Complex conjugate and transpose matrix equation; Relaxed gradient based iterative algorithm; Relaxation factor; Optimal factor; LEAST-SQUARES SOLUTIONS; ALGORITHM; CONJUGATE; IDENTIFICATION; STABILIZATION; DECOMPOSITION; A(I)XB(I);
D O I：
10.1007/s12190-020-01486-6
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
Wu et al. (Applied Mathematics and Computation 217(2011)8343-8353) constructed a gradient based iterative (GI) algorithm to find the solution to the complex conjugate and transpose matrix equation A(1)XB(1) + A(2)(X) over barB(2) + A(3)X(T)B(3) + A(4)X(H)B(4) = E and a sufficient condition for guaranteeing the convergence of GI algorithm was given for an arbitrary initial matrix. Zhang et al. (Journal of the Franklin Institute 354 (2017) 7585-7603) provided a new proof of GI method and the necessary and sufficient conditions was presented to guarantee that the proposed algorithm was convergent for an arbitrary initial matrix. In this paper, a relaxed gradient based iterative (RGI) algorithm is proposed to solve this complex conjugate and transpose matrix equation. The necessary and sufficient conditions for the convergence factor is determined to guarantee the convergence of the introduced algorithm for any initial iterative matrix. Numerical results are given to verify the efficiency of the new method. Finally, the application in time-varying linear system of the presented algorithm is provided.
引用
收藏
页码：317 / 341
页数：25
相关论文
共 50 条
  • [1] Iterative solution to a class of complex matrix equations and its application in time-varying linear system
    Wang, Wenli
    Song, Caiqin
    Ji, Shipu
    Journal of Applied Mathematics and Computing, 2021, 67 (1-2): : 317 - 341
  • [2] Iterative solution to a class of complex matrix equations and its application in time-varying linear system
    Wenli Wang
    Caiqin Song
    Shipu Ji
    Journal of Applied Mathematics and Computing, 2021, 67 : 317 - 341
  • [3] Improved Zhang neural network model and its solution of time-varying generalized linear matrix equations
    Li, Zhan
    Zhang, Yunong
    EXPERT SYSTEMS WITH APPLICATIONS, 2010, 37 (10) : 7213 - 7218
  • [4] An Improved Finite Time Convergence Recurrent Neural Network with Application to Time-Varying Linear Complex Matrix Equation Solution
    Jin, Jie
    NEURAL PROCESSING LETTERS, 2021, 53 (01) : 777 - 786
  • [5] An Improved Finite Time Convergence Recurrent Neural Network with Application to Time-Varying Linear Complex Matrix Equation Solution
    Jie Jin
    Neural Processing Letters, 2021, 53 : 777 - 786
  • [6] Adaptive iterative learning control for a class of linear time-varying systems
    College of Mathematic and Physics, Qingdao University of Science and Technology, Qingdao, China
    不详
    Int. J. Comput. Sci. Issues, 5 5-1 (61-66):
  • [7] Iterative learning control for a class of nonlinear time-varying system
    Li, Xiang-Yang, 1600, South China University of Technology (31):
  • [8] Finite-time Convergent Complex-Valued Neural Networks for the Time-varying Complex Linear Matrix Equations
    Wang, Xuezhong
    Liang, Lu
    Che, Maolin
    ENGINEERING LETTERS, 2018, 26 (04)
  • [9] Nonlinear recurrent neural networks for finite-time solution of general time-varying linear matrix equations
    Xiao, Lin
    Liao, Bolin
    Li, Shuai
    Chen, Ke
    NEURAL NETWORKS, 2018, 98 : 102 - 113
  • [10] Exponential stability of switched linear impulsive time-varying system and its application
    Ju, Yanhao
    Meng, Fanwei
    Sun, Yuangong
    JOURNAL OF THE FRANKLIN INSTITUTE-ENGINEERING AND APPLIED MATHEMATICS, 2022, 359 (11): : 5619 - 5633
12345