论文标题
针对非线性方程系统的柄和安德森型加速技术
Shanks and Anderson-type acceleration techniques for systems of nonlinear equations
论文作者
论文摘要
本文研究了许多推断和加速方法，并介绍了与一般序列相关的标准小腿转换的一些修改。本文的目标之一是制定一个涵盖大多数已知加速策略的一般框架。本文还考虑了新的光线下的安德森加速度方法，并利用了准牛顿方法的联系，以建立安德森加速方法稳定版本的局部线性收敛结果。这些方法在许多问题上进行了测试，其中包括由非线性部分微分方程产生的一些问题。
This paper examines a number of extrapolation and acceleration methods, and introduces a few modifications of the standard Shanks transformation that deal with general sequences. One of the goals of the paper is to lay out a general framework that encompasses most of the known acceleration strategies. The paper also considers the Anderson Acceleration method under a new light and exploits a connection with quasi-Newton methods, in order to establish local linear convergence results of a stabilized version of Anderson Acceleration method. The methods are tested on a number of problems, including a few that arise from nonlinear Partial Differential Equations.
