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.

翻译：在本文中,我们为安德森加速度开发了趋同和加速理论,用于牛顿的非线性系统方法,在非线性系统中,雅各布人是一个单一的解决方案。对于这些问题,标准的牛顿算法在有关解决方案的区域中直线趋同;以及以前曾观察到,安德森加速度可以大大改进趋同,而不增加先验知识,也不增加额外的计算成本。我们在此背景下对牛顿-安德森算法进行了分析,并引入了一种新颖和理论上支持的保障战略。与Chandrashekar H-equation和一些标准基准范例一起展示了趋同结果。