| 尹素素,欧阳自根.求解最小二乘问题的带动量的Gauss-Seidel方法[J].南华大学学报(自然科学版),2023,(5):81~86, 96.[YIN Susu,OUYANG Zigen.Gauss-Seidel Method with Momentum for Solving Least-Squares Problems[J].Journal of University of South China(Science and Technology),2023,(5):81~86, 96.] |
| 求解最小二乘问题的带动量的Gauss-Seidel方法 |
| Gauss-Seidel Method with Momentum for Solving Least-Squares Problems |
| 投稿时间：2023-06-27 |
| DOI：10.19431/j.cnki. 1673-0062.2023.05.012 |
| 中文关键词: 最小二乘问题 Gauss-Seidel方法 动量 |
| 英文关键词:least squares problem Gauss-Seidel method momentum |
| 基金项目:湖南省自然科学基金项目(2019JJ40240) |
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| 中文摘要: |
| 最小二乘问题是重要的数学与统计模型,广泛用于回归分析、参数估计、最优控制和数据拟合等领域。基于古典的Gauss-Seidel方法,推导了求解最小二乘问题的迭代格式。结合Gauss-Seidel方法和Polyak's Heavy-Ball技术,提出了动量型Gauss-Seidel方法的算法框架。根据贪婪的策略选择指标,建立了贪婪的动量型Gauss-Seidel方法的线性收敛性。最后,数值实验表明贪婪的动量型Gauss-Seidel方法在迭代步数和计算时间方面均优于贪婪的Gauss-Seidel方法。 |
| 英文摘要: |
| The least-squares problem is an important mathematical and statistical model, which is widely used in regression analysis, parameter estimation, optimal control and data fitting. Based on the classical Gauss-Seidel method, the iterative scheme for solving the least-squares problem is deduced. Combining Gauss-Seidel method and Polyak's Heavy-Ball technique, an algorithm framework of Gauss-Seidel method with momentum is proposed. The linear convergence of the greedy Gauss-Seidel method with momentum is established by selecting the column index according to the greedy strategy. Finally, numerical experiments show that the greedy Gauss-Seidel method with momentum outperforms the greedy Gauss-Seidel method in terms of iteration steps and computation time. |
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