We propose a new class of multi-layer iterative schemes for solving sparse linear systems in saddle point structure. The new scheme consist of an iterative preconditioner that is based on the (approximate) nullspace method, combined with an iterative least squares approach and an iterative projection method. We present a theoretical analysis and demonstrate the effectiveness and robustness of the new scheme on sparse matrices from various applications.

翻译：本文提出了一类新的多层迭代方案，用于求解具有鞍点结构的稀疏线性系统。该新方案包含一个基于（近似）零空间方法的迭代预处理器，并结合了迭代最小二乘方法与迭代投影方法。我们给出了理论分析，并在来自不同应用的稀疏矩阵上验证了新方案的有效性与鲁棒性。