论文标题
关于三分三块马鞍点问题的预处理
On the preconditioning of three-by-three block saddle point problems
论文作者
论文摘要
我们建立了一种新的迭代方法，用于求解具有具有鞍点结构的三个块系数矩阵的大型和稀疏的线性方程式。研究了所提出的方法的收敛性能，并研究了其诱导的预处理，以加快广义最小残留（GMRE）方法的收敛速度。更确切地说，我们分析了预处理矩阵的特征值分布。据报道，数值实验证明了所提出的预处理的有效性。
We establish a new iterative method for solving a class of large and sparse linear systems of equations with three-by-three block coefficient matrices having saddle point structure. Convergence properties of the proposed method are studied in details and its induced preconditioner is examined for accelerating the convergence speed of generalized minimal residual (GMRES) method. More precisely, we analyze the eigenvalue distribution of the preconditioned matrix. Numerical experiments are reported to demonstrate the effectiveness of the proposed preconditioner.
