Based on the equivalent transformation of the complex coefficient matrix, a fully structured preconditioner which is economic to implement within GMRES acceleration is presented for solving a class of complex symmetric indefinite linear systems. We analyze the computational complexity of the proposed preconditioner and show that all eigenvalues of the corresponding preconditioned matrix are clustered at a top half annulus. Compared with some other existing preconditioners, the validity of theoretical analysis and the effectiveness of the proposed preconditioner are verified by numerical experiments.

中文翻译：

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一类复杂对称不定线性系统的全结构预处理器

基于复系数矩阵的等效变换，提出了一种在GMRES加速中实现经济的全结构化预处理器，用于求解一类复对称不定线性系统。我们分析了所提出的预处理器的计算复杂性，并表明相应的预处理矩阵的所有特征值都聚集在上半环上。与其他一些现有的预处理器相比，通过数值实验验证了理论分析的有效性和所提出的预处理器的有效性。