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 algorithm under a new light and exploits a connection with Quasi-Newton methods, in order to establish local linear convergence results of Anderson-type techniques . The methods are tested on a number of problems, including a few that arise from nonlinear Partial Differential Equations.
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.
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acceleration algorithm
Acceleration method
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Quasi-Newton
quasi-Newton
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Anderson-type techniques
a stabilized version of Anderson Acceleration method