| 康靖,马昌凤.Sylvester矩阵方程的改进IO迭代算法[J].井冈山大学自然版,2023,44(2):1-8 |
| Sylvester矩阵方程的改进IO迭代算法 |
| IMPROVED IO ITERATIVE ALGORITHM FOR SYLVESTER MATRIX EQUATION |
| 投稿时间：2022-04-07 修订日期：2022-05-25 |
| DOI：10.3969/j.issn.1674-8085.2023.02.001 |
| 中文关键词: Sylvester矩阵方程 IO迭代算法 Smith算法 收敛性 迭代因子 |
| 英文关键词: Sylvester matrix equations IO iteration algorithm Smith method convergence iteration factors |
| 基金项目:国家自然科学基金项目(11901098)；福建省自然科学基金项目(2020J05034) |
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| 中文摘要: |
| 通过对Sylvester矩阵方程的理论分析，可知IO迭代算法中迭代矩阵的谱半径随内迭代次数的增大而减小，更新了IO迭代算法中内迭代次数的选择方法，并证明了该算法收敛性与初始矩阵无关。Sylvester矩阵在满足一些特定条件下，为了进一步提高收敛速度，可通过选择适当的相关参数，使得IO迭代算法有较好的收敛速度且比Smith算法的迭代次数明显减少。 |
| 英文摘要: |
| Through the theoretical analysis of the Sylvester matrix equation, it is known that the spectral radius of the iterative matrix in the IO iteration algorithm decreases with the increase of the number of inner iterations. The selection method of the number of inner iterations in the IO iteration algorithm is updated, and the convergence of the algorithm is proved to be independent of the initial matrix. When the Sylvester matrix satisfies some specific conditions, in order to further improve the convergence speed, by selecting appropriate relevant parameters, the IO iteration algorithm has a better convergence speed and the number of iterations is significantly reduced than that of the Smith algorithm. |
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