The HSS splitting hierarchical identification algorithms for solving the Sylvester matrix equation

Huiling Wang; Zhaolu Tian; Yufeng Nie; Huiling Wang; Zhaolu Tian; Yufeng Nie

doi:10.3934/math.2025605

AIMS Mathematics

2025, Volume 10, Issue 6: 13476-13497. doi: 10.3934/math.2025605

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Research article

The HSS splitting hierarchical identification algorithms for solving the Sylvester matrix equation

1.
College of Applied Mathematics, Shanxi University of Finance and Economics, Taiyuan 030006, China
2.
School of Mathematics and Statistics, Northwestern Polytechnical University, Xi'an 710072, China

Received: 07 March 2025 Revised: 02 June 2025 Accepted: 04 June 2025 Published: 12 June 2025
MSC : 15A24, 65F30

By combining the hierarchical identification principle with HSS splitting, we presented the HSS splitting hierarchical identification algorithm for solving the Sylvester matrix equation in this paper. To enhance the convergence rate of the algorithm, the momentum item was introduced in the iteration. We conducted an in-depth analysis of the sufficient conditions that ensured the convergence properties of the proposed algorithms. Additionally, the optimal parameters involved in the algorithms were computed exactly in each iteration by the minimum residual technique for specific cases. Thus, the adaptive forms of the corresponding algorithms were obtained. Finally, several numerical examples were implemented to demonstrate the superiority and effectiveness of the designed algorithms in this paper.
- hierarchical identification principle,
- Hermitian and skew-Hermitian splitting,
- the minimum residual technique,
- momentum,
- optimal parameters
Citation: Huiling Wang, Zhaolu Tian, Yufeng Nie. The HSS splitting hierarchical identification algorithms for solving the Sylvester matrix equation[J]. AIMS Mathematics, 2025, 10(6): 13476-13497. doi: 10.3934/math.2025605

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Abstract

By combining the hierarchical identification principle with HSS splitting, we presented the HSS splitting hierarchical identification algorithm for solving the Sylvester matrix equation in this paper. To enhance the convergence rate of the algorithm, the momentum item was introduced in the iteration. We conducted an in-depth analysis of the sufficient conditions that ensured the convergence properties of the proposed algorithms. Additionally, the optimal parameters involved in the algorithms were computed exactly in each iteration by the minimum residual technique for specific cases. Thus, the adaptive forms of the corresponding algorithms were obtained. Finally, several numerical examples were implemented to demonstrate the superiority and effectiveness of the designed algorithms in this paper.

References

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