求解复对称线性方程组的新分裂迭代方法及预处理子(英文)

A New Splitting and Preconditioner for Iteratively Solving a Class of Complex Symmetric Linear Systems

本文提出求解系数矩阵为复对称但非埃尔米特的线性方程组的一种新分裂迭代法,研究新迭代矩阵的谱半径及最优参数选择,证明在合理的条件下新方法的收敛性,并讨论预处理子的条件数,最后以数值实验验证新方法的有效性和可行性.

A new splitting iteration method is presented for the system of linear equations when the coefficient matrix is a non-Hermitian but symmetric complex matrix. The optimal parameter and the spectral radius properties of the iteration matrix for the new method are discussed in detail. Based on these results, the new method is convergent under reasonable conditions for a class of complex symmetric linear systems. With the results obtained, we show that the new method is convergent for a class of complex symmetric linear system and propose a preconditioner to improve the condition number of the system. Finally, the numerical experiment show the new method to be feasible and effective.