{"ID":2854865,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2510.15097","arxiv_id":"2510.15097","title":"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.","short_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...","url_abs":"https://arxiv.org/abs/2510.15097","url_pdf":"https://arxiv.org/pdf/2510.15097v2","authors":"[\"Kazufumi Ito\",\"Tiancheng Xue\"]","published":"2025-10-16T19:35:25Z","proceeding":"math.NA","tasks":"[\"math.NA\",\"math.OC\"]","methods":"[]","has_code":false}