论文标题
牛顿·安德森（Newton-Anderson）
Newton-Anderson at Singular Points
论文作者
论文摘要
在本文中，我们开发了安德森加速度的融合和加速理论，应用于牛顿的非线性系统方法，其中雅各布在解决方案上是单数。对于这些问题，标准的牛顿算法在解决方案的区域中线性收敛。而且，以前已经观察到，安德森加速度可以在没有其他先验知识的情况下基本上改善收敛性，而且几乎没有额外的计算成本。在这种情况下，我们对牛顿 - 安德森算法进行了分析，并介绍了一种小说和理论上支持的保护策略。 Chandrasekhar H-方程和一些标准基准示例证明了收敛结果。
In this paper we develop convergence and acceleration theory for Anderson acceleration applied to Newton's method for nonlinear systems in which the Jacobian is singular at a solution. For these problems, the standard Newton algorithm converges linearly in a region about the solution; and, it has been previously observed that Anderson acceleration can substantially improve convergence without additional a priori knowledge, and with little additional computation cost. We present an analysis of the Newton-Anderson algorithm in this context, and introduce a novel and theoretically supported safeguarding strategy. The convergence results are demonstrated with the Chandrasekhar H-equation and some standard benchmark examples.
