SOR迭代阵的谱半径的上界及收敛性分析(英文)

A Bound for Spectral Radius and Convergence of SOR Iterative Matrices

针对线性方程组Ax=b在求解时常用的SOR迭代方法,给出了SOR迭代矩阵谱半径的新的上界及迭代法中参数的收敛性区域,并将其收敛区域推广到H矩阵情形.该上界优于已有的结果,给出数值例子说明所得结果的优越性.

For solving linear equations Ax=b,a new bound for spectral radius of SOR iterative matrices, based on the concept of doubly diagonal dominance is presented.As an application of the bound,a practical convergence condition of SOR method is obtained.The results obtained are an improvement of those in Ref.[1] and suitable for an extended matrix class,i.e.,doubly diagonally dominant matrices.The results arc also generalized to H-matrices.