求解大型线性最小二乘问题的贪婪Gauss-Seidel方法

A Greedy Gauss-Seidel Method for Solving the Large Linear Least Squares Problem

摘要:

基于一种选择系数矩阵A的工作列的策略，提出了求解大型线性最小二乘问题的一种不同的贪婪Gauss-Seidel方法，并对该方法进行了收敛性分析。数值实验表明，在相同的精度下，所提方法在计算时间上优于文献提出的贪婪随机坐标下降方法。

关键词:贪婪Gauss-Seidel方法;贪婪随机坐标下降方法;随机的Gauss-Seidel方法;大型线性最小二乘问题

Abstract:

An alternative greedy Gauss-Seidel method for solving the large linear least squares problem is proposed based on a novel strategy for choosing the working columns of the coefficient matrix A， and the convergence of the new method is analyzed. The numerical experiments show that for the same accuracy， the method proposed in this paper outperforms the greedy randomized coordinate descent method proposed recently in term of the computing time.

Key words:greedy Gauss-Seidel method;greedy randomized coordinate descent method;randomized Gauss-Seidel method;large linear least squares problem