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 (AA) 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 the AA method. The methods are tested on a number of problems, including a few that arise from nonlinear partial differential equations.

中文翻译：

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非线性方程组的 Shanks 和 Anderson 型加速技术

本文研究了许多外推和加速方法，并介绍了处理一般序列的标准 Shanks 变换的一些修改。本文的目标之一是制定一个包含大多数已知加速策略的通用框架。本文还从新的角度考虑了安德森加速度 (AA) 方法，并利用与准牛顿方法的联系来建立稳定版本的 AA 方法的局部线性收敛结果。这些方法在许多问题上进行了测试，包括一些由非线性偏微分方程引起的问题。