论文标题
通过预处理的迭代方法求解$（a +γuu^t）\，{\ bf x} = {\ bf x} = {\ bf x} $的线性系统
Solving linear systems of the form $(A + γUU^T)\, {\bf x} = {\bf b}$ by preconditioned iterative methods
论文作者
论文摘要
我们考虑了大型线性方程式的迭代解决方案，其中系数矩阵是两个术语的总和，一个稀疏的矩阵$ a $和可能是$γuu^t $的形式的密集，等级不足的矩阵，其中$γ> 0 $，其中某些$ $ a $ a $ a的$ a $ a是一个$ a $ a的参数。半决赛和$ a+γuu^t $是非词。该形式的线性系统经常出现在优化，流体力学，计算统计等领域。我们研究了基于交替分裂方法的预处理策略，并结合使用Sherman-Morrison-Woodbury矩阵身份。通过在不同应用领域的线性系统上进行数值实验证明了所提出的方法的潜力。
We consider the iterative solution of large linear systems of equations in which the coefficient matrix is the sum of two terms, a sparse matrix $A$ and a possibly dense, rank deficient matrix of the form $γUU^T$, where $γ> 0$ is a parameter which in some applications may be taken to be 1. The matrix $A$ itself can be singular, but we assume that the symmetric part of $A$ is positive semidefinite and that $A+γUU^T$ is nonsingular. Linear systems of this form arise frequently in fields like optimization, fluid mechanics, computational statistics, and others. We investigate preconditioning strategies based on an alternating splitting approach combined with the use of the Sherman-Morrison-Woodbury matrix identity. The potential of the proposed approach is demonstrated by means of numerical experiments on linear systems from different application areas.
