Improved modified gradient-based iterative algorithm and its relaxed version for the complex conjugate and transpose Sylvester matrix equations
In this article, we present two new algorithms referred to as the improved modified gradient-based iterative (IMGI) algorithm and its relaxed version (IMRGI) for solving the complex conjugate and transpose (CCT) Sylvester matrix equations, which often arise from control theory, system theory, and so...
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
De Gruyter
2024-11-01
|
| Series: | Demonstratio Mathematica |
| Subjects: | |
| Online Access: | https://doi.org/10.1515/dema-2024-0083 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1846143534518763520 |
|---|---|
| author | Huang Zhengge Cui Jingjing |
| author_facet | Huang Zhengge Cui Jingjing |
| author_sort | Huang Zhengge |
| collection | DOAJ |
| description | In this article, we present two new algorithms referred to as the improved modified gradient-based iterative (IMGI) algorithm and its relaxed version (IMRGI) for solving the complex conjugate and transpose (CCT) Sylvester matrix equations, which often arise from control theory, system theory, and so forth. Compared with the gradient-based iterative (GI) (A.-G. Wu, L.-L. Lv, and G.-R. Duan, Iterative algorithms for solving a class of complex conjugate and transpose matrix equations, Appl. Math. Comput. 217 (2011), 8343–8353) and the relaxed GI (RGI) (W.-L. Wang, C.-Q. Song, and S.-P. Ji, Iterative solution to a class of complex matrix equations and its application in time-varying linear system, J. Appl. Math. Comput. 67 (2021), 317–341) algorithms, the proposed ones can make full use of the latest information and need less computations, which leads to higher computational efficiency. With the real representation of a complex matrix as a tool, we establish sufficient and necessary conditions for the convergence of the IMGI and the IMRGI algorithms. Finally, some numerical examples are given to illustrate the effectiveness and advantages of the proposed algorithms. |
| format | Article |
| id | doaj-art-d8dc1ecb17084ebfa981f8eb47605e11 |
| institution | Kabale University |
| issn | 2391-4661 |
| language | English |
| publishDate | 2024-11-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Demonstratio Mathematica |
| spelling | doaj-art-d8dc1ecb17084ebfa981f8eb47605e112024-12-02T12:03:38ZengDe GruyterDemonstratio Mathematica2391-46612024-11-015719911010.1515/dema-2024-0083Improved modified gradient-based iterative algorithm and its relaxed version for the complex conjugate and transpose Sylvester matrix equationsHuang Zhengge0Cui Jingjing1School of Mathematical Sciences, Center for Applied Mathematics of Guangxi, Guangxi Minzu University, 530006, Nanning, P. R. ChinaSchool of Mathematical Sciences, Center for Applied Mathematics of Guangxi, Guangxi Minzu University, 530006, Nanning, P. R. ChinaIn this article, we present two new algorithms referred to as the improved modified gradient-based iterative (IMGI) algorithm and its relaxed version (IMRGI) for solving the complex conjugate and transpose (CCT) Sylvester matrix equations, which often arise from control theory, system theory, and so forth. Compared with the gradient-based iterative (GI) (A.-G. Wu, L.-L. Lv, and G.-R. Duan, Iterative algorithms for solving a class of complex conjugate and transpose matrix equations, Appl. Math. Comput. 217 (2011), 8343–8353) and the relaxed GI (RGI) (W.-L. Wang, C.-Q. Song, and S.-P. Ji, Iterative solution to a class of complex matrix equations and its application in time-varying linear system, J. Appl. Math. Comput. 67 (2021), 317–341) algorithms, the proposed ones can make full use of the latest information and need less computations, which leads to higher computational efficiency. With the real representation of a complex matrix as a tool, we establish sufficient and necessary conditions for the convergence of the IMGI and the IMRGI algorithms. Finally, some numerical examples are given to illustrate the effectiveness and advantages of the proposed algorithms.https://doi.org/10.1515/dema-2024-0083complex conjugate and transpose matrix equationimproved modified gradient-based iterative algorithmimproved modified relaxed gradient-based iterative algorithmconvergence conditionreal representation65f1065h10 |
| spellingShingle | Huang Zhengge Cui Jingjing Improved modified gradient-based iterative algorithm and its relaxed version for the complex conjugate and transpose Sylvester matrix equations Demonstratio Mathematica complex conjugate and transpose matrix equation improved modified gradient-based iterative algorithm improved modified relaxed gradient-based iterative algorithm convergence condition real representation 65f10 65h10 |
| title | Improved modified gradient-based iterative algorithm and its relaxed version for the complex conjugate and transpose Sylvester matrix equations |
| title_full | Improved modified gradient-based iterative algorithm and its relaxed version for the complex conjugate and transpose Sylvester matrix equations |
| title_fullStr | Improved modified gradient-based iterative algorithm and its relaxed version for the complex conjugate and transpose Sylvester matrix equations |
| title_full_unstemmed | Improved modified gradient-based iterative algorithm and its relaxed version for the complex conjugate and transpose Sylvester matrix equations |
| title_short | Improved modified gradient-based iterative algorithm and its relaxed version for the complex conjugate and transpose Sylvester matrix equations |
| title_sort | improved modified gradient based iterative algorithm and its relaxed version for the complex conjugate and transpose sylvester matrix equations |
| topic | complex conjugate and transpose matrix equation improved modified gradient-based iterative algorithm improved modified relaxed gradient-based iterative algorithm convergence condition real representation 65f10 65h10 |
| url | https://doi.org/10.1515/dema-2024-0083 |
| work_keys_str_mv | AT huangzhengge improvedmodifiedgradientbasediterativealgorithmanditsrelaxedversionforthecomplexconjugateandtransposesylvestermatrixequations AT cuijingjing improvedmodifiedgradientbasediterativealgorithmanditsrelaxedversionforthecomplexconjugateandtransposesylvestermatrixequations |