Two Relaxed Gradient-Based Algorithms for the Hermitian and Skew-Hermitian Solutions of the Linear Matrix Equation AXB + CXD = F
| Autor: | Ahmed M. E. Bayoumi |
|---|---|
| Rok vydání: | 2019 |
| Předmět: |
0209 industrial biotechnology
Iterative method General Mathematics General Physics and Astronomy Linear matrix equation 010103 numerical & computational mathematics 02 engineering and technology General Chemistry 01 natural sciences Hermitian matrix Matrix (mathematics) 020901 industrial engineering & automation Skew-Hermitian matrix Gradient based algorithm General Earth and Planetary Sciences Mathematics::Differential Geometry 0101 mathematics General Agricultural and Biological Sciences Algorithm Mathematics |
| Zdroj: | Iranian Journal of Science and Technology, Transactions A: Science. 43:2343-2350 |
| ISSN: | 2364-1819 1028-6276 |
| DOI: | 10.1007/s40995-019-00694-5 |
| Popis: | In this paper, two relaxed gradient-based algorithms for solving the linear matrix equation $$ AXB + CXD = F $$ and finding the Hermitian and skew-Hermitian solutions are presented. We proved that the algorithms converge to the Hermitian and skew-Hermitian solutions. A sufficient condition is given to guarantee that the solutions given by the proposed algorithms converge to the Hermitian and skew-Hermitian solutions for any initial matrix. Two numerical examples are given to test its efficiency and accuracy compared with our proposed modification of the gradient-based iterative algorithm proposed in Ding et al. (Appl Math Comput 197(1):41–50, 2008). |
| Databáze: | OpenAIRE |
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