Iterative solution to a class of complex matrix equations and its application in time-varying linear system
Iterative solution to a class of complex matrix equations and its application in time-varying linear system
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一类复矩阵方程的迭代求解及其在时变线性系统中的应用
DOI：
10.1007/s12190-020-01486-6
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发表时间：
2021-01
影响因子：
2.2
通讯作者：
Shipu Ji
中科院分区：
文献类型：
--
作者：
Wenli Wang;Caiqin Song;Shipu Ji
Wu et al. （Applied Mathematics and Computation 217(2011)8343-8353）构造了一种基于梯度的迭代（GI）算法求解复共轭转置矩阵方程$$\begin{aligned} A_{1}XB_{1}+A_{2}\overline{X}B_{2}+A_{3}X^{T}B_{3}+A_{4}X^{H}B_{4}=E \end{aligned}$$，并给出了对于任意初始矩阵GI算法收敛的充分条件。Zhang et al. （Journal of the Franklin Institute 354(2017) 7585-7603）提供了一种新的GI方法证明，并给出了保证算法对任意初始矩阵收敛的充分必要条件。本文提出了一种基于松弛梯度的迭代（RGI）算法来求解这类复杂的共轭和转置矩阵方程。确定了收敛因子的充分必要条件，保证算法对任意初始迭代矩阵收敛。数值结果验证了该方法的有效性。最后，给出了该算法在时变线性系统中的应用。
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 $$\begin{aligned} A_{1}XB_{1}+A_{2}\overline{X}B_{2}+A_{3}X^{T}B_{3}+A_{4}X^{H}B_{4}=E \end{aligned}$$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.
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DOI：
10.1007/1-4020-2721-4_1
发表时间：
2011-04
期刊：
--
影响因子：
--
作者：
B. Ya
通讯作者：
B. Ya
影响因子：
2.4
作者：
Zhuo-Heng He;Qing-Wen Wang;Yang Zhang
通讯作者：
Yang Zhang
影响因子：
2.4
作者：
Q. Niu;Xiang Wang;Linzhang Lu
通讯作者：
Q. Niu;Xiang Wang;Linzhang Lu
影响因子：
1.8
作者：
M. Hajarian
通讯作者：
M. Hajarian
影响因子：
6.8
作者：
Bin Zhou;G. Duan
通讯作者：
Bin Zhou;G. Duan