关于大型线性最小二乘问题的自适应确定性块坐标下降带动量方法
数值分析
2024-10-29 v1 数值分析
摘要
在本工作中，我们首先提出了一种基于 Polyak 重心法和新列选择准则的自适应确定性块坐标下降方法带动量 (mADBCD)，用于求解线性最小二乘问题，该方法基于残差向量的欧几里得范数定义的一组块受控索引。mADBCD 方法消除了对列索引系数矩阵进行预分区的需求，也消除了在每次迭代中计算列子矩阵的 Moore-Penrose 伪逆的需求。此外，我们展示了 mADBCD 方法在自动选择和更新块控制索引集方面的适应性和灵活性。当系数矩阵具有满秩时，mADBCD 方法的理论分析表明其对线性最小二乘问题的唯一解线性收敛。 Furthermore, by effectively integrating count sketch technology with the mADBCD method, we also propose a novel count sketch adaptive block coordinate descent method with momentum (CS-mADBCD) for solving highly overdetermined linear least-squares problems and analysis its convergence. Finally, numerical experiments illustrate the advantages of the proposed two methods in terms of both CPU times and iteration counts compared to recent block coordinate descent methods.
引用
@article{arxiv.2410.20108,
title = {On the adaptive deterministic block coordinate descent methods with momentum for solving large linear least-squares problems},
author = {Long-Ze Tan and Ming-Yu Deng and Jia-Li Qiu and Xue-Ping Guo},
journal= {arXiv preprint arXiv:2410.20108},
year = {2024}
}