Based on the single-step iteration (SSI) method for the non-Hermitian positive definite linear systems, we propose a Uzawa-SSI method for solving the saddle point problems with non-Hermitian positive definite (1, 1) block in this paper. The convergence and semi-convergence properties of the Uzawa-SSI method, respectively, for nonsingular and singular cases are analyzed. Numerical examples with experiments are given to show the robustness and the efficiency of Uzawa-SSI method.

中文翻译：

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关于非Hermitian鞍点问题的Uzawa-SSI方法

基于非Hermitian正定线性系统的单步迭代（SSI）方法，本文提出了一种求解非Hermitian正定（1，1）块鞍点问题的Uzawa-SSI方法。分析了非奇异情况和奇异情况下Uzawa-SSI方法的收敛性和半收敛性。数值算例表明了Uzawa-SSI方法的鲁棒性和有效性。