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  1. Free, publicly-accessible full text available September 20, 2024
  2. Abstract 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. 
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