用AOR方法求解大型稀疏最小二乘问题的收敛性

ON CONVERGENCE OF AOR METHODS FOR LARGE SPARSE LEAST-SQUARES PROBLEMS

在许多实际问题中,我们都希望计算以下超定线性方程组 Ax=b (1)的最小二乘解.其中A为一大型疏m×n实矩阵,m>n,b为一给定的m维实向量.这里假定Rank(A)=n. 我们知道,(1)可叙述成,求唯一向量X∈R^n,使||b—AX||_2=min||b—Ay||_2对一切y∈R^n。由于Rank(A)=n。

The convergence of SOR methods and SSOR methods for solving a least-squares problemwith a large sparse coefficient matrix has already been proved [1-4]. In this paper, the con-vergence of AOR methods for solving the equation generated by least-squares problems is con-sidered. It is shown that, by properly selecting the parameters, the AOR methods are always con-vergent.