| 王茜,马昌凤.求解Sylvester矩阵方程的加速SSJGI方法[J].井冈山大学自然版,2025,46(3):1-7 |
| 求解Sylvester矩阵方程的加速SSJGI方法 |
| ACCELERATED SSJGI METHOD FOR SOLVING SYLVESTER MATRIX EQUATIONS |
| 投稿时间：2025-01-13 修订日期：2025-02-21 |
| DOI：10.3969/j.issn.1674-8085.2025.03.001 |
| 中文关键词: Sylvester矩阵方程 SSJGI算法 加速SSJGI算法 收敛性分析 数值实验 |
| 英文关键词: Sylvester matrix equation SSJGI algorithm acceleration of the SSJGI algorithm convergence analysis numerical experiments |
| 基金项目:国家自然科学基金项目(12371378)；福建省自然科学基金项目(2024J01980) |
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| 中文摘要: |
| 基于求解Sylvester矩阵方程的移位分裂雅可比迭代方法（SSJGI算法)及其收敛性的已有研究。本研究进一步将加速技术引入SSJGI算法求解Sylvester矩阵方程，构建了加速SSJGI算法，并对该算法进行收敛性分析。数值实验表明，加速SSJGI算法与SSJGI算法比较，能够较快地减少残差，达到较高的精度，具有更好的收敛性能。 |
| 英文摘要: |
| Based on the study of the Shifted Split Jacobi Iteration method (SSJGI algorithm) for solving Sylvester matrix equations and its convergence properties, this paper further incorporates acceleration techniques into the SSJGI algorithm to enhance the solution process for Sylvester matrix equations. An accelerated SSJGI algorithm is developed, and a convergence analysis of this algorithm is conducted. Numerical experiments demonstrate that the accelerated SSJGI algorithm significantly reduces residuals more rapidly, achieves higher precision, and exhibits superior convergence performance. |
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