Reduced order method based Anderson-type acceleration method for nonlinear least square problems and large scale ill-posed problems
Abstract
In this paper, we propose an acceleration framework for a class of iterative methods using the Reduced Order Method (ROM). Assuming that the underlying iterative scheme generates a rich basis for the solution space, we construct the next iterate by minimizing the equation error over the linear manifold spanned by this basis. The resulting optimal linear combination yields a more accurate approximation of the solution and significantly enhances convergence. In essence, the method can be seen as a history-based acceleration technique, akin to a delayed or memory-enhanced iterative scheme. This approach effectively remedies semi-ill-posed problems, enabling convergence where standard methods may fail, and also acts as a stabilizing and regularizing mechanism for the original iteration.
Cite
@article{arxiv.2510.15097,
title = {Reduced order method based Anderson-type acceleration method for nonlinear least square problems and large scale ill-posed problems},
author = {Kazufumi Ito and Tiancheng Xue},
journal= {arXiv preprint arXiv:2510.15097},
year = {2025}
}