In this paper, based on the simplified Hermitian and skew-Hermitian (SHSS) preconditioner, a new preconditioner, called the generalized SHSS (GSHSS) preconditioner, is considered to solve the generalized saddle point problem. We prove that the GSHSS iteration method is convergent if the iteration parameters satisfy appropriate conditions. In addition, it is proved that all eigenvalues of the GSHSS preconditioned matrix are real and non-unit eigenvalues are located in a positive interval. Numerical experiment is provided to show the effectiveness of the GSHSS preconditioner.

中文翻译：

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广义鞍点问题的广义SHSS预处理器

本文基于简化的Hermitian和skew-Hermitian（SHSS）预处理器，考虑了一种称为广义SHSS（GSHSS）预处理器的新预处理器，以解决广义鞍点问题。如果迭代参数满足适当的条件，我们证明了GSSHS迭代方法是收敛的。此外，证明了GSHSS预处理矩阵的所有特征值都是真实的，非单位特征值位于正区间。数值实验表明了GSSHS预处理器的有效性。