Two accelerated gradient-based iteration methods for solving the Sylvester matrix equation AX + XB = C
In this paper, combining the precondition technique and momentum item with the gradient-based iteration algorithm, two accelerated iteration algorithms are presented for solving the Sylvester matrix equation $ AX+XB = C $. Sufficient conditions to guarantee the convergence properties of the proposed...
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| Format: | Article |
| Language: | English |
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AIMS Press
2024-12-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.20241654 |
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| author | Huiling Wang Nian-Ci Wu Yufeng Nie |
| author_facet | Huiling Wang Nian-Ci Wu Yufeng Nie |
| author_sort | Huiling Wang |
| collection | DOAJ |
| description | In this paper, combining the precondition technique and momentum item with the gradient-based iteration algorithm, two accelerated iteration algorithms are presented for solving the Sylvester matrix equation $ AX+XB = C $. Sufficient conditions to guarantee the convergence properties of the proposed algorithms are analyzed in detail. Varying the parameters of these algorithms in each iteration, the corresponding adaptive iteration algorithms are also provided, and the adaptive parameters can be explicitly obtained by the minimum residual technique. Several numerical examples are implemented to illustrate the effectiveness of the proposed algorithms. |
| format | Article |
| id | doaj-art-e43a25a0421f4975ae87f6fa8e2adfcd |
| institution | Kabale University |
| issn | 2473-6988 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj-art-e43a25a0421f4975ae87f6fa8e2adfcd2025-01-23T07:53:25ZengAIMS PressAIMS Mathematics2473-69882024-12-01912347343475210.3934/math.20241654Two accelerated gradient-based iteration methods for solving the Sylvester matrix equation AX + XB = CHuiling Wang0Nian-Ci Wu1Yufeng Nie2College of Applied Mathematics, Shanxi University of Finance and Economics, Taiyuan 030006, ChinaSchool of Mathematics and Statistics, South-Central Minzu University, Wuhan 430074, ChinaSchool of Mathematics and Statistics, Northwestern Polytechnical University, Xi'an 710072, ChinaIn this paper, combining the precondition technique and momentum item with the gradient-based iteration algorithm, two accelerated iteration algorithms are presented for solving the Sylvester matrix equation $ AX+XB = C $. Sufficient conditions to guarantee the convergence properties of the proposed algorithms are analyzed in detail. Varying the parameters of these algorithms in each iteration, the corresponding adaptive iteration algorithms are also provided, and the adaptive parameters can be explicitly obtained by the minimum residual technique. Several numerical examples are implemented to illustrate the effectiveness of the proposed algorithms.https://www.aimspress.com/article/doi/10.3934/math.20241654sylvester matrix equationgradient-based iterationmomentum termprecondition techniqueminimum residual technique |
| spellingShingle | Huiling Wang Nian-Ci Wu Yufeng Nie Two accelerated gradient-based iteration methods for solving the Sylvester matrix equation AX + XB = C AIMS Mathematics sylvester matrix equation gradient-based iteration momentum term precondition technique minimum residual technique |
| title | Two accelerated gradient-based iteration methods for solving the Sylvester matrix equation AX + XB = C |
| title_full | Two accelerated gradient-based iteration methods for solving the Sylvester matrix equation AX + XB = C |
| title_fullStr | Two accelerated gradient-based iteration methods for solving the Sylvester matrix equation AX + XB = C |
| title_full_unstemmed | Two accelerated gradient-based iteration methods for solving the Sylvester matrix equation AX + XB = C |
| title_short | Two accelerated gradient-based iteration methods for solving the Sylvester matrix equation AX + XB = C |
| title_sort | two accelerated gradient based iteration methods for solving the sylvester matrix equation ax xb c |
| topic | sylvester matrix equation gradient-based iteration momentum term precondition technique minimum residual technique |
| url | https://www.aimspress.com/article/doi/10.3934/math.20241654 |
| work_keys_str_mv | AT huilingwang twoacceleratedgradientbasediterationmethodsforsolvingthesylvestermatrixequationaxxbc AT nianciwu twoacceleratedgradientbasediterationmethodsforsolvingthesylvestermatrixequationaxxbc AT yufengnie twoacceleratedgradientbasediterationmethodsforsolvingthesylvestermatrixequationaxxbc |