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.
翻译:本文件审查了一些外推法和加速法,并对标准Shanks转换法作了一些修改,涉及一般序列。文件的目标之一是提出一个包含大多数已知加速战略的总框架。文件还审议了在新光线下采用Anderson加速法的问题,并探讨了与准Newton法的联系,以便确定稳定版本的Anderson加速法的局部线性趋同结果。这些方法在若干问题上进行了测试,包括一些非线性局部差异产生的问题。