Benchmarking results for the Newton–Anderson method
Benchmarking results for the Newton–Anderson method
复制标题
牛顿安德森方法的基准测试结果
DOI：
10.1016/j.rinam.2020.100095
复制
发表时间：
2020
影响因子：
2
通讯作者：
Schwartz, Hunter
中科院分区：
文献类型：
--
作者：
Pollock, Sara;Schwartz, Hunter
本文主要介绍了安德森加速牛顿法在一组基准问题上的数值结果。结果证明了对退化和非退化问题的解的超线性收敛。非退化问题的收敛性在理论上也是合理的。对于退化问题，即那些雅可比行列式在解上是奇异的问题，我们研究收敛域。在这种情况下观察到牛顿-安德森具有与牛顿相似的收敛域，但如果问题稍微受到扰动，它可能会被不同于牛顿的解决方案所吸引。
This paper primarily presents numerical results for the Anderson accelerated Newton method on a set of benchmark problems. The results demonstrate superlinear convergence to solutions of both degenerate and nondegenerate problems. The convergence for nondegenerate problems is also justified theoretically. For degenerate problems, those whose Jacobians are singular at a solution, the domain of convergence is studied. It is observed in that setting that Newton–Anderson has a domain of convergence similar to Newton, but it may be attracted to a different solution than Newton if the problems are slightly perturbed.