论文标题
SPD线性系统的紧凑型准Newton预处理
Compact Quasi-Newton preconditioners for SPD linear systems
论文作者
论文摘要
在本文中，研究了共轭梯度方法的预处理，以用对称的正确定雅各布式解决牛顿系统。特别是，我们定义了一系列通过SR1和BFG构建的预处理序列。我们开发了SR1更新维护预处理SPD的条件。 SR1预处理的雅各布人的光谱分析显示，随着牛顿迭代的进行，特征值分布得到了改善。开发了预处理更新的紧凑型矩阵公式，该公式降低了其应用程序的成本，并且更适合并行实施。给出了一些有关实现牛顿方法的实现的注释，许多模型问题的数值结果说明了提出的预处理的效率。
In this paper preconditioners for the Conjugate Gradient method are studied to solve the Newton system with symmetric positive definite Jacobian. In particular, we define a sequence of preconditioners built by means of SR1 and BFGS low-rank updates. We develop conditions under which the SR1 update maintains the preconditioner SPD. Spectral analysis of the SR1 preconditioned Jacobians shows an improved eigenvalue distribution as the Newton iteration proceeds. A compact matrix formulation of the preconditioner update is developed which reduces the cost of its application and is more suitable for parallel implementation. Some notes on the implementation of the corresponding Inexact Newton method are given and numerical results on a number of model problems illustrate the efficiency of the proposed preconditioners.
