@Article{IJNAM-20-667,
author = {Dallas , Matt and Pollock , Sara},
title = {Newton-Anderson at Singular Points},
journal = {International Journal of Numerical Analysis and Modeling},
year = {2023},
volume = {20},
number = {5},
pages = {667--692},
abstract = {<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>},
issn = {2617-8710},
doi = {https://doi.org/10.4208/ijnam2023-1029},
url = {http://global-sci.org/intro/article_detail/ijnam/22007.html}
}