论文标题
基于误差矢量采样的线性系统的误差矢量采样，对预处理的CG求解器的收敛加速度
Convergence Acceleration of Preconditioned CG Solver Based on Error Vector Sampling for a Sequence of Linear Systems
论文作者
论文摘要
在本文中，我们专注于解决具有相同（或相似）系数矩阵的线性系统的序列。对于这种类型的问题，我们研究了子空间校正和通缩方法，这些方法使用辅助矩阵（子空间）来加速迭代方法的收敛性。在实际模拟中，当辅助矩阵的范围包含对应于系数矩阵的小特征值的特征空间时，这些加速度方法通常会很好地工作。我们已经开发了一种基于误差矢量采样的新代数辅助矩阵构造方法，其中在解决方案过程中有效地鉴定了具有小特征值的特征向量。生成的辅助矩阵用于以下解决方案步骤中的收敛加速度。数值测试证实，使用辅助矩阵的子空间校正和缩放方法都可以加速迭代求解器的溶液过程。此外，我们研究了我们技术对系数矩阵条件数估计的适用性。还显示了具有条件号估计的预处理共轭梯度（PCG）方法的算法。
In this paper, we focus on solving a sequence of linear systems with an identical (or similar) coefficient matrix. For this type of problems, we investigate the subspace correction and deflation methods, which use an auxiliary matrix (subspace) to accelerate the convergence of the iterative method. In practical simulations, these acceleration methods typically work well when the range of the auxiliary matrix contains eigenspaces corresponding to small eigenvalues of the coefficient matrix. We have developed a new algebraic auxiliary matrix construction method based on error vector sampling, in which eigenvectors with small eigenvalues are efficiently identified in a solution process. The generated auxiliary matrix is used for the convergence acceleration in the following solution step. Numerical tests confirm that both subspace correction and deflation methods with the auxiliary matrix can accelerate the solution process of the iterative solver. Furthermore, we examine the applicability of our technique to the estimation of the condition number of the coefficient matrix. The algorithm of preconditioned conjugate gradient (PCG) method with the condition number estimation is also shown.
