求解复对称线性系统的CRI变型迭代法

A Variant of the CRI Iteration Method for a Class of Complex Symmetric Linear Systems

讨论了求解复对称线性系统的CRI迭代法,进一步提出了CRI变型迭代法,并给出了该迭代法的收敛性和最优收敛因子的证明。发现当CRI迭代法和CRI变型迭代法分别取最优参数以及线性系统满足一定条件时,CRI变型迭代法迭代矩阵的谱半径比CRI迭代法迭代矩阵的谱半径更小。数值实验进一步验证了CRI变型迭代法的有效性。

In this paper, we mainly discuss the CRI iteration method for a class of complex symmetric linear systems, further propose a variant of the CRI iteration method, and prove the convergence of the iteration method and its optimal convergence factor. Meanwhile, we find that the spectral radius of the iteration matrix of the variant of the CRI iteration method is smaller than that of the CRI iteration method if the CRI iteration method and the variant of the CRI iteration method take the optimal parameters respectively while the linear systems satisfy certain conditions. The numerical experiment further verifies the validity of the variant of the CRI iteration method.