Abstract: In this paper, the convergence rate of stationary two-stage iterative methods is studied. Comparison results about the convergence rate of stationary two-stage iterative methods and their outer iterative methods are obtained. It is shown that the outer iterative methods are faster than the stationary two-stage iterative methods with the mild splittings. For the splittings of H-matrices, comparison results are also gotten. Finally, the obtained results are illustrated by the example.

Key words: stationary two-stage iterative method, outer iterative method, irreducible matrix, H-matrix, spectral radius

摘要： 研究了定常二级迭代法的收敛性，得到了定常二级迭代法与其外迭代收敛率的比较定理。结果表明外迭代的收敛速度一般快于定常二级迭代法，还给出了H-矩阵迭代法的比较结论。最后，数值例子验证了结论。

关键词: 定常二级迭代法, 外迭代法, 不可约矩阵, H-矩阵, 谱半径