Izvorni znanstveni članak

https://doi.org/10.1080/00051144.2024.2362050

The relaxed gradient based iterative algorithm for solving the generalized coupled complex conjugate and transpose Sylvester matrix equations

Yanping Long ; Faculty of Mathematics and Physics, Guangxi Minzu University, Guangxi, People’s Republic of China
Jingjing Cui ; Faculty of Mathematics and Physics, Guangxi Minzu University, Guangxi, People’s Republic of China *
Zhengge Huang ; Faculty of Mathematics and Physics, Guangxi Minzu University, Guangxi, People’s Republic of China
Xiaowen Wu ; Faculty of Mathematics and Physics, Guangxi Minzu University, Guangxi, People’s Republic of China

* Dopisni autor.

Sažetak

Inspired by the idea of Ma et al. (Journal of the Franklin Institute, 2018), we adopt relaxation
technique and introduce relaxation factors into the gradient based iterative (GI) algorithm, and
the relaxed based iterative (RGI) algorithm is established to solve the generalized coupled complex conjugate and transpose Sylvester matrix equations. By applying the real representation
and straighten operation, we contain the sufficient and necessary condition for convergence of
the RGI method. In order to effectively utilize this algorithm, we further derive the optimal convergence parameter and some related conclusions. Moreover, to overcome the high dimension
calculation problem, a sufficient condition for convergence with less computational complexity is determined. Finally, numerical examples are reported to demonstrate the availability and
superiority of the constructed iterative algorithm.

Ključne riječi

Generalized coupled complex conjugate and transpose matrix equations; relaxed gradient based iterative algorithm; convergence analysis; optimal convergence parameter

Hrčak ID:

326276

URI

https://hrcak.srce.hr/326276

Datum izdavanja:

5.6.2024.

Posjeta: 0 *