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

作　　者：尹素素 欧阳自根[1] YIN Susu;OUYANG Zigen(School of Mathmatics and Physics,University of South China,Hengyang,Hunan 421001,China)

机构地区：[1]南华大学数理学院,湖南衡阳421001

出　　处：《南华大学学报（自然科学版）》2023年第5期81-86,96,共7页Journal of University of South China：Science and Technology

基　　金：湖南省自然科学基金项目(2019JJ40240)。

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。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 Polyaks 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.

关 键 词：最小二乘问题 Gauss-Seidel方法 动量 

分 类 号：O241.6[理学—计算数学]