论文标题
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
A two-level iterative scheme for general sparse linear systems based on approximate skew-symmetrizers
论文作者
论文摘要
我们提出了一个两级迭代方案，用于解决一般稀疏线性系统。所提出的方案由一个稀疏的预处理组成，该方案增加了偏斜的部分，并使系数矩阵的主要对角线尽可能接近身份。然后，通过特定的最小残留方法来解决预处理系统（MRS）。这导致了两级（内部和外部）迭代方案，其中MRS具有短期复发并满足最佳条件。内部系统的预处理是通过基于偏斜的朗索斯工艺的偏斜对称策略来设计的。我们证明了提出的方案对来自各种应用的稀疏矩阵的鲁棒性。
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.
