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

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...

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Vydané v:	AIMS mathematics Ročník 10; číslo 6; s. 13476 - 13497
Hlavní autori:	Wang, Huiling, Tian, Zhaolu, Nie, Yufeng
Médium:	Journal Article
Jazyk:	English
Vydavateľské údaje:	AIMS Press 01.06.2025
Predmet:	hermitian and skew-hermitian splitting hierarchical identification principle momentum optimal parameters the minimum residual technique
ISSN:	2473-6988, 2473-6988
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Shrnutí:	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.
ISSN:	2473-6988 2473-6988
DOI:	10.3934/math.2025605