TY - JOUR
T1 - Newton-Anderson at Singular Points
AU - Dallas , Matt
AU - Pollock , Sara
JO - International Journal of Numerical Analysis and Modeling
VL - 5
SP - 667
EP - 692
PY - 2023
DA - 2023/09
SN - 20
DO - http://doi.org/10.4208/ijnam2023-1029
UR - https://global-sci.org/intro/article_detail/ijnam/22007.html
KW - Anderson acceleration, Newton’s method, safeguarding, singular problems.
AB - <p style="text-align: justify;">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.</p>