Accelerated Implicit Single-Step Splitting Iteration Method for a Class of Coupled Lyapunov Equations
For the coupled Lyapunov problem derived from continuous Markov jump systems, a new implicit single-step splitting(ISS) iterative algorithm is proposed based on the idea of single step split iteration. After that, the accelerated implicit single-step splitting(AISS) iterative method, which is an acc...
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| Format: | Article |
| Language: | English |
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IEEE
2020-01-01
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| Series: | IEEE Access |
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| Online Access: | https://ieeexplore.ieee.org/document/9204371/ |
| _version_ | 1831558605659176960 |
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| author | Shi-Yu Li Xin-Hui Shao Yan-Ran Li |
| author_facet | Shi-Yu Li Xin-Hui Shao Yan-Ran Li |
| author_sort | Shi-Yu Li |
| collection | DOAJ |
| description | For the coupled Lyapunov problem derived from continuous Markov jump systems, a new implicit single-step splitting(ISS) iterative algorithm is proposed based on the idea of single step split iteration. After that, the accelerated implicit single-step splitting(AISS) iterative method, which is an accelerated algorithm of ISS iterative method, is proposed by using the idea of two-step alternate iteration. In this paper, the relevant convergence proofs of ISS and AISS iteration methods are given. Then, the selection range of the parameters of ISS and AISS iteration methods and the selection method of optimal parameters are given. Finally, this paper demonstrates the feasibility and advantage of the novel methods through actual calculations. |
| first_indexed | 2024-12-17T05:13:30Z |
| format | Article |
| id | doaj.art-92cc57b0f7a74c7a83d94a0f5afbe4b4 |
| institution | Directory Open Access Journal |
| issn | 2169-3536 |
| language | English |
| last_indexed | 2024-12-17T05:13:30Z |
| publishDate | 2020-01-01 |
| publisher | IEEE |
| record_format | Article |
| series | IEEE Access |
| spelling | doaj.art-92cc57b0f7a74c7a83d94a0f5afbe4b42022-12-21T22:02:11ZengIEEEIEEE Access2169-35362020-01-01817159017159710.1109/ACCESS.2020.30249179204371Accelerated Implicit Single-Step Splitting Iteration Method for a Class of Coupled Lyapunov EquationsShi-Yu Li0https://orcid.org/0000-0002-6660-1760Xin-Hui Shao1https://orcid.org/0000-0002-4120-8428Yan-Ran Li2Department of Mathematics, Northeastern University, Shenyang, ChinaDepartment of Mathematics, Northeastern University, Shenyang, ChinaDepartment of Mathematics, Northeastern University, Shenyang, ChinaFor the coupled Lyapunov problem derived from continuous Markov jump systems, a new implicit single-step splitting(ISS) iterative algorithm is proposed based on the idea of single step split iteration. After that, the accelerated implicit single-step splitting(AISS) iterative method, which is an accelerated algorithm of ISS iterative method, is proposed by using the idea of two-step alternate iteration. In this paper, the relevant convergence proofs of ISS and AISS iteration methods are given. Then, the selection range of the parameters of ISS and AISS iteration methods and the selection method of optimal parameters are given. Finally, this paper demonstrates the feasibility and advantage of the novel methods through actual calculations.https://ieeexplore.ieee.org/document/9204371/Continuous Markov jump systemscoupled Lyapunov matrix equationsISS iterative algorithmAISS iterative method |
| spellingShingle | Shi-Yu Li Xin-Hui Shao Yan-Ran Li Accelerated Implicit Single-Step Splitting Iteration Method for a Class of Coupled Lyapunov Equations IEEE Access Continuous Markov jump systems coupled Lyapunov matrix equations ISS iterative algorithm AISS iterative method |
| title | Accelerated Implicit Single-Step Splitting Iteration Method for a Class of Coupled Lyapunov Equations |
| title_full | Accelerated Implicit Single-Step Splitting Iteration Method for a Class of Coupled Lyapunov Equations |
| title_fullStr | Accelerated Implicit Single-Step Splitting Iteration Method for a Class of Coupled Lyapunov Equations |
| title_full_unstemmed | Accelerated Implicit Single-Step Splitting Iteration Method for a Class of Coupled Lyapunov Equations |
| title_short | Accelerated Implicit Single-Step Splitting Iteration Method for a Class of Coupled Lyapunov Equations |
| title_sort | accelerated implicit single step splitting iteration method for a class of coupled lyapunov equations |
| topic | Continuous Markov jump systems coupled Lyapunov matrix equations ISS iterative algorithm AISS iterative method |
| url | https://ieeexplore.ieee.org/document/9204371/ |
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