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.
Original language | English (US) |
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Pages (from-to) | 3058-3093 |
Number of pages | 36 |
Journal | IMA Journal of Numerical Analysis |
Volume | 42 |
Issue number | 4 |
DOIs | |
State | Published - Oct 1 2022 |
Externally published | Yes |
Bibliographical note
Publisher Copyright:© The Author(s) 2021.
Keywords
- Anderson acceleration
- Krylov subspace methods
- Navier–Stokes equation
- extrapolation methods
- nonlinear Poisson problems
- quasi-Newton methods
- regularization