This paper introduces a preconditioned method designed to comprehensively address the saddle point system with the aim of improving convergence efficiency. In the preprocessor construction phase, a technical approach for solving the approximate inverse matrix of sparse matrices is presented. The effectiveness of the proposed method is demonstrated through numerical examples, emphasizing its efficacy in approximating the inverse matrix. Furthermore, the preprocessing technology includes a low-rank processing step, effectively reducing algorithmic complexity. Numerical experiments validate the effectiveness and feasibility of PSLR-GMRES in solving the saddle point system.

翻译：本文提出了一种旨在全面解决鞍点系统的预条件方法，以提高收敛效率。在预处理器构建阶段，给出了一种求解稀疏矩阵近似逆矩阵的技术方案。通过数值算例验证了所提方法的有效性，重点突出了其在矩阵求逆近似中的效能。此外，该预处理技术包含低秩处理步骤，有效降低了算法复杂度。数值实验验证了PSLR-GMRES在求解鞍点系统中的有效性和可行性。