  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.
