【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。更多还原

【Abstract】 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.更多还原