Newton-Anderson at Singular Points

Newton-Anderson at Singular Points

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.

Author Details

Matt Dallas

Sara Pollock