In this paper, we introduce a preconditioned Euler-extrapolated single-step Hermitian and skew-Hermitian splitting (PE-SHSS) iteration method for solving a class of complex symmetric system of linear equations. The convergence properties of the PE-SHSS iteration method are investigated under suitable restrictions. In addition, the spectral properties of the corresponding preconditioned matrix are discussed. Finally, three numerical examples are also used to verify the effectiveness of the PE-SHSS iteration method.

中文翻译：

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复杂对称线性系统的预处理欧拉外推单步厄米和斜厄米分裂方法

在本文中，我们介绍了一种用于求解一类复杂对称线性方程组的预处理欧拉外推单步 Hermitian 和 skew-Hermitian 分裂 (PE-SHSS) 迭代方法。在适当的限制下研究了 PE-SHSS 迭代方法的收敛特性。此外，还讨论了相应的预处理矩阵的光谱特性。最后，还通过三个数值算例验证了PE-SHSS迭代方法的有效性。