PHSS Iterative Method for Solving Generalized Lyapunov Equations
Based on previous research results, we propose a new preprocessing HSS iteration method (PHSS) for the generalized Lyapunov equation. At the same time, the corresponding inexact PHSS algorithm (IPHSS) is given from the angle of application. All the new methods presented in this paper have given the...
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| Format: | Article |
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MDPI AG
2019-01-01
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| Series: | Mathematics |
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| Online Access: | http://www.mdpi.com/2227-7390/7/1/38 |
| _version_ | 1831701515152130048 |
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| author | Shi-Yu Li Hai-Long Shen Xin-Hui Shao |
| author_facet | Shi-Yu Li Hai-Long Shen Xin-Hui Shao |
| author_sort | Shi-Yu Li |
| collection | DOAJ |
| description | Based on previous research results, we propose a new preprocessing HSS iteration method (PHSS) for the generalized Lyapunov equation. At the same time, the corresponding inexact PHSS algorithm (IPHSS) is given from the angle of application. All the new methods presented in this paper have given the corresponding convergence proof. The numerical experiments are carried out to compare the new method with the existing methods, and the improvement effect is obvious. The feasibility and effectiveness of the proposed method are proved from two aspects of theory and calculation. |
| first_indexed | 2024-12-20T15:04:08Z |
| format | Article |
| id | doaj.art-18357f64ae1745a6b5d120e1bf2af26d |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-12-20T15:04:08Z |
| publishDate | 2019-01-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-18357f64ae1745a6b5d120e1bf2af26d2022-12-21T19:36:34ZengMDPI AGMathematics2227-73902019-01-01713810.3390/math7010038math7010038PHSS Iterative Method for Solving Generalized Lyapunov EquationsShi-Yu Li0Hai-Long Shen1Xin-Hui Shao2Department of Mathematics, College of Sciences, Northeastern University, Shenyang 110819, ChinaDepartment of Mathematics, College of Sciences, Northeastern University, Shenyang 110819, ChinaDepartment of Mathematics, College of Sciences, Northeastern University, Shenyang 110819, ChinaBased on previous research results, we propose a new preprocessing HSS iteration method (PHSS) for the generalized Lyapunov equation. At the same time, the corresponding inexact PHSS algorithm (IPHSS) is given from the angle of application. All the new methods presented in this paper have given the corresponding convergence proof. The numerical experiments are carried out to compare the new method with the existing methods, and the improvement effect is obvious. The feasibility and effectiveness of the proposed method are proved from two aspects of theory and calculation.http://www.mdpi.com/2227-7390/7/1/38Lyapunov equationHSS iterative methodPHSS iterative method |
| spellingShingle | Shi-Yu Li Hai-Long Shen Xin-Hui Shao PHSS Iterative Method for Solving Generalized Lyapunov Equations Mathematics Lyapunov equation HSS iterative method PHSS iterative method |
| title | PHSS Iterative Method for Solving Generalized Lyapunov Equations |
| title_full | PHSS Iterative Method for Solving Generalized Lyapunov Equations |
| title_fullStr | PHSS Iterative Method for Solving Generalized Lyapunov Equations |
| title_full_unstemmed | PHSS Iterative Method for Solving Generalized Lyapunov Equations |
| title_short | PHSS Iterative Method for Solving Generalized Lyapunov Equations |
| title_sort | phss iterative method for solving generalized lyapunov equations |
| topic | Lyapunov equation HSS iterative method PHSS iterative method |
| url | http://www.mdpi.com/2227-7390/7/1/38 |
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