Year: 2023
Author: Matt Dallas, Sara Pollock
International Journal of Numerical Analysis and Modeling, Vol. 20 (2023), Iss. 5 : pp. 667–692
Abstract
In this paper we develop convergence and acceleration theory for Anderson acceleration applied to Newton’s method for nonlinear systems in which the Jacobian is singular at a solution. For these problems, the standard Newton algorithm converges linearly in a region about the solution; and, it has been previously observed that Anderson acceleration can substantially improve convergence without additional a priori knowledge, and with little additional computation cost. We present an analysis of the Newton-Anderson algorithm in this context, and introduce a novel and theoretically supported safeguarding strategy. The convergence results are demonstrated with the Chandrasekhar H-equation and a variety of benchmark examples.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/ijnam2023-1029
International Journal of Numerical Analysis and Modeling, Vol. 20 (2023), Iss. 5 : pp. 667–692
Published online: 2023-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 26
Keywords: Anderson acceleration Newton’s method safeguarding singular problems.