A RELAXED GRADIENT BASED ALGORITHM FOR SOLVING SYLVESTER EQUATIONS

被引：86
|
作者：
Niu, Qiang [1 ]
Wang, Xiang [2 ]
Lu, Lin-Zhang [3 ,4 ]
机构：
[1] Xian Jiaotong Liverpool Univ, MPTC, Suzhou 215123, Peoples R China
[2] Nanchang Univ, Dept Math, Nanchang 330047, Peoples R China
[3] Guizhou Normal Univ, Sch Math & Comp Sci, Guiyang 550001, Peoples R China
[4] Xiamen Univ, Sch Math Sci, Xiamen 361005, Peoples R China
来源：
ASIAN JOURNAL OF CONTROL | 2011年 / 13卷 / 03期
基金：
中国国家自然科学基金;
关键词：
Sylvester equation; iterative method; relaxation parameter; IDENTIFICATION;
D O I：
10.1002/asjc.328
中图分类号：
TP [自动化技术、计算机技术];
学科分类号：
0812 ;
摘要：
By introducing a relaxation parameter, we derive a relaxed gradient based iterative algorithm for solving Sylvester equations. Theoretical analysis shows that the new method converges under certain assumptions. Comparisons are performed with the original algorithm, and results show that the new method exhibits fast convergence behavior with a wide range of relaxation parameters.
引用
收藏
页码：461 / 464
页数：4
相关论文
共 50 条
  • [1] A relaxed gradient based algorithm for solving generalized coupled Sylvester matrix equations
    Sheng, Xingping
    JOURNAL OF THE FRANKLIN INSTITUTE-ENGINEERING AND APPLIED MATHEMATICS, 2018, 355 (10): : 4282 - 4297
  • [2] A RELAXED GRADIENT BASED ALGORITHM FOR SOLVING EXTENDED SYLVESTER-CONJUGATE MATRIX EQUATIONS
    Ramadan, Mohamed A.
    El-Danaf, Talaat S.
    Bayoumi, Ahmed M. E.
    ASIAN JOURNAL OF CONTROL, 2014, 16 (05) : 1334 - 1341
  • [3] A modified gradient based algorithm for solving Sylvester equations
    Wang, Xiang
    Dai, Lin
    Liao, Dan
    APPLIED MATHEMATICS AND COMPUTATION, 2012, 218 (09) : 5620 - 5628
  • [4] The relaxed gradient based iterative algorithm for solving the generalized coupled complex conjugate and transpose Sylvester matrix equations
    Long, Yanping
    Cui, Jingjing
    Huang, Zhengge
    Wu, Xiaowen
    AUTOMATIKA, 2024, 65 (03) : 1241 - 1258
  • [5] The relaxed gradient based iterative algorithm for solving matrix equations AiXBi = Fi
    Sheng, Xingping
    Sun, Weiwei
    COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2017, 74 (03) : 597 - 604
  • [6] An Accelerated Jacobi-gradient Based Iterative Algorithm for Solving Sylvester Matrix Equations
    Tian, Zhaolu
    Tian, Maoyi
    Gu, Chuanqing
    Hao, Xiaoning
    FILOMAT, 2017, 31 (08) : 2381 - 2390
  • [7] A modified gradient-based algorithm for solving extended Sylvester-conjugate matrix equations
    Ramadan, Mohamed A.
    Bayoumi, Ahmed M. E.
    ASIAN JOURNAL OF CONTROL, 2018, 20 (01) : 228 - 235
  • [8] The Weighted, Relaxed Gradient-Based Iterative Algorithm for the Generalized Coupled Conjugate and Transpose Sylvester Matrix Equations
    Wu, Xiaowen
    Huang, Zhengge
    Cui, Jingjing
    Long, Yanping
    AXIOMS, 2023, 12 (11)
  • [9] Conjugate gradient-based iterative algorithm for solving generalized periodic coupled Sylvester matrix equations
    Chen, Zebin
    Chen, Xuesong
    JOURNAL OF THE FRANKLIN INSTITUTE-ENGINEERING AND APPLIED MATHEMATICS, 2022, 359 (17): : 9925 - 9951
  • [10] An accelerated gradient-based iterative algorithm for solving extended Sylvester-conjugate matrix equations
    Bayoumi, Ahmed M. E.
    Ramadan, Mohamed A.
    TRANSACTIONS OF THE INSTITUTE OF MEASUREMENT AND CONTROL, 2018, 40 (01) : 341 - 347
12345