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. 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.