We propose a two-level iterative scheme for solving general sparse linear systems. The proposed scheme consists of a sparse preconditioner that increases the skew-symmetric part and makes the main diagonal of the coefficient matrix as close to the identity as possible. The preconditioned system is then solved via a particular Minimal Residual Method for Shifted Skew-Symmetric Systems (mrs). This leads to a two-level (inner and outer) iterative scheme where the mrs has short term recurrences and satisfies an optimally condition. A preconditioner for the inner system is designed via a skew-symmetry preserving deflation strategy based on the skew-Lanczos process. We demonstrate the robustness of the proposed scheme on sparse matrices from various applications.

中文翻译：

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基于近似偏斜对称器的一般稀疏线性系统的两级迭代方案

我们提出了一种用于解决一般稀疏线性系统的两级迭代方案。所提出的方案包括一个稀疏预处理器，它增加了偏对称部分并使系数矩阵的主对角线尽可能接近恒等式。然后通过特定的最小残差移动偏斜对称系统 (mrs) 方法求解预处理系统。这导致了两级（内部和外部）迭代方案，其中 mrs 具有短期重复并满足最佳条件。内部系统的预处理器是通过基于 skew-Lanczos 过程的 skew-symmetry 保持紧缩策略设计的。我们证明了所提出方案在来自各种应用的稀疏矩阵上的稳健性。