| 郑月桂,黄宝华.松弛贪婪随机块Kaczmarz方法求解四元数线性系统[J].井冈山大学自然版,2025,(5):12-18 |
| 松弛贪婪随机块Kaczmarz方法求解四元数线性系统 |
| RELAXED GREEDY RANDOMIZED BLOCK KACZMARZ METHOD FOR SOLVING QUATERNION LINEAR SYSTEMS |
| 投稿时间：2025-03-03 修订日期：2025-04-11 |
| DOI：10.3969/j.issn.1674-8085.2025.05.002 |
| 中文关键词: 四元数线性系统 随机块Kaczmarz方法 松弛贪婪选择策略 收敛性分析 |
| 英文关键词: quaternion linear systems randomized block Kaczmarz method relaxed greedy selection strategy convergence analysis |
| 基金项目:国家自然科学基金青年项目(12001211) |
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| 中文摘要: |
| 随机块Kaczmarz方法是一种用于求解大规模线性系统的迭代方法，其核心在于每次迭代都将当前迭代点正交投影到约束子集的求解空间上。本研究提出了一种四元数松弛贪婪随机块Kaczmarz(QRGRBK)迭代方法，并建立了收敛性理论，用于求解四元数线性系统。通过数值实验，验证了QRGRBK方法的可行性和有效性。此外，还展示了QRGRBK方法在图像恢复中的应用，证明了该方法在实际问题中的实用性和高效性。 |
| 英文摘要: |
| The randomized block Kaczmarz method is an iterative method for solving large-scale linear systems.At each iteration, the algorithm orthogonally projects the current iteration point onto the solution space of the constrained subset. This study proposes a relaxed greedy randomized block Kaczmarz（QRGRBK） method for the quaternion linear systems and proves its convergence. Through numerical experiments, the feasibility and effectiveness of the QRGRBK method have been successfully validated. Furthermore, the application of the QRGRBK method in image restoration has been demonstrated, which provides substantial evidence for its practical utility and computational efficiency in real-world scenarios. |
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