A Successive over Relaxation Implicit Iterative Algorithm for Solving Stochastic Linear Systems with Markov Jumps
In order to solve continuous stochastic Lyapunov equations, a novel implicit iterative algorithm is presented by means of successive over relaxation (SOR) iteration in this article. Throughout this method, three tuning parameters are added for the improvement of the convergence rate. It is shown tha...
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| Format: | Article |
| Language: | English |
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MDPI AG
2024-04-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/12/7/1080 |
| _version_ | 1827286733440417792 |
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| author | Tianrui Wu Peiqi Huang Hong Chen |
| author_facet | Tianrui Wu Peiqi Huang Hong Chen |
| author_sort | Tianrui Wu |
| collection | DOAJ |
| description | In order to solve continuous stochastic Lyapunov equations, a novel implicit iterative algorithm is presented by means of successive over relaxation (SOR) iteration in this article. Throughout this method, three tuning parameters are added for the improvement of the convergence rate. It is shown that this algorithm is monotonically bounded, and the convergence condition is also given and extended. Applying the latest updated estimates, this algorithm can attain a better convergence performance compared with other existing iterative algorithms when choosing appropriate tuning parameters. Finally, a numerical example is provided to illustrate the feasibility and priority of this approach. |
| first_indexed | 2024-04-24T10:39:36Z |
| format | Article |
| id | doaj.art-eb82611306ce4d8b818216d9b7df393f |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-04-24T10:39:36Z |
| publishDate | 2024-04-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-eb82611306ce4d8b818216d9b7df393f2024-04-12T13:22:49ZengMDPI AGMathematics2227-73902024-04-01127108010.3390/math12071080A Successive over Relaxation Implicit Iterative Algorithm for Solving Stochastic Linear Systems with Markov JumpsTianrui Wu0Peiqi Huang1Hong Chen2School of Science, Nanjing Forestry University, Nanjing 210037, ChinaSchool of Science, Nanjing Forestry University, Nanjing 210037, ChinaSchool of Science, Nanjing Forestry University, Nanjing 210037, ChinaIn order to solve continuous stochastic Lyapunov equations, a novel implicit iterative algorithm is presented by means of successive over relaxation (SOR) iteration in this article. Throughout this method, three tuning parameters are added for the improvement of the convergence rate. It is shown that this algorithm is monotonically bounded, and the convergence condition is also given and extended. Applying the latest updated estimates, this algorithm can attain a better convergence performance compared with other existing iterative algorithms when choosing appropriate tuning parameters. Finally, a numerical example is provided to illustrate the feasibility and priority of this approach.https://www.mdpi.com/2227-7390/12/7/1080iterative algorithmsSORcontinuous stochastic Lyapunov equationsMarkov jumps |
| spellingShingle | Tianrui Wu Peiqi Huang Hong Chen A Successive over Relaxation Implicit Iterative Algorithm for Solving Stochastic Linear Systems with Markov Jumps Mathematics iterative algorithms SOR continuous stochastic Lyapunov equations Markov jumps |
| title | A Successive over Relaxation Implicit Iterative Algorithm for Solving Stochastic Linear Systems with Markov Jumps |
| title_full | A Successive over Relaxation Implicit Iterative Algorithm for Solving Stochastic Linear Systems with Markov Jumps |
| title_fullStr | A Successive over Relaxation Implicit Iterative Algorithm for Solving Stochastic Linear Systems with Markov Jumps |
| title_full_unstemmed | A Successive over Relaxation Implicit Iterative Algorithm for Solving Stochastic Linear Systems with Markov Jumps |
| title_short | A Successive over Relaxation Implicit Iterative Algorithm for Solving Stochastic Linear Systems with Markov Jumps |
| title_sort | successive over relaxation implicit iterative algorithm for solving stochastic linear systems with markov jumps |
| topic | iterative algorithms SOR continuous stochastic Lyapunov equations Markov jumps |
| url | https://www.mdpi.com/2227-7390/12/7/1080 |
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