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- Title
The Weighted, Relaxed Gradient-Based Iterative Algorithm for the Generalized Coupled Conjugate and Transpose Sylvester Matrix Equations.
- Authors
Wu, Xiaowen; Huang, Zhengge; Cui, Jingjing; Long, Yanping
- Abstract
By applying the weighted relaxation technique to the gradient-based iterative (GI) algorithm and taking proper weighted combinations of the solutions, this paper proposes the weighted, relaxed gradient-based iterative (WRGI) algorithm to solve the generalized coupled conjugate and transpose Sylvester matrix equations. With the real representation of a complex matrix as a tool, the necessary and sufficient conditions for the convergence of the WRGI algorithm are determined. Also, some sufficient convergence conditions of the WRGI algorithm are presented. Moreover, the optimal step size and the corresponding optimal convergence factor of the WRGI algorithm are given. Lastly, some numerical examples are provided to demonstrate the effectiveness, feasibility and superiority of the proposed algorithm.
- Subjects
SYLVESTER matrix equations; RELAXATION techniques; COMPLEX matrices; ALGORITHMS
- Publication
Axioms (2075-1680), 2023, Vol 12, Issue 11, p1062
- ISSN
2075-1680
- Publication type
Article
- DOI
10.3390/axioms12111062