基于 Sherman-Morrison-Woodbury 方法的低秩更新最小二乘问题求解
数值分析
2024-07-02 v2 数值分析
摘要
我们提出了一种用于更新全秩矩形矩阵伪逆的简单公式，以应对低秩修改情况，并展示了其在求解最小二乘问题中的实用性。 resulting algorithm can be dramatically faster than solving the modified least squares problem from scratch, just like the speedup enabled by Sherman--Morrison--Woodbury for solving linear systems with low-rank modifications. 这种算法就像Sherman-Morrison-Woodbury方法在求解具有低秩修改的线性系统时所带来的加速效果一样，能够显著加快求解速度。
引用
@article{arxiv.2406.15120,
title = {A Sherman--Morrison--Woodbury approach to solving least squares problems with low-rank updates},
author = {Stefan Güttel and Yuji Nakatsukasa and Marcus Webb and Alban Bloor Riley},
journal= {arXiv preprint arXiv:2406.15120},
year = {2024}
}
备注
6 pages