论文标题
通过不确定性量化实用实用的大规模随机迭代最小二乘求解器
Towards Practical Large-scale Randomized Iterative Least Squares Solvers through Uncertainty Quantification
论文作者
论文摘要
随着用于实验设计的问题和数据的规模，信号处理和数据同化的增长，通常的最小二乘子问题在大小上相应地增长。由于这些最小二乘问题的规模会为通常的增量QR和基于Krylov的算法创造出良好的记忆运动成本，因此随机的最小二乘问题问题引起了更多的关注。但是，这些随机的最小二乘求解器很难将应用算法整合在一起，因为它们的不确定性限制了算法进度和可靠停止的实际跟踪。因此，在这项工作中，我们开发了理论上符合性的实用工具，以量化重要的一类重要的迭代随机最小二乘算法的不确定性，然后我们使用它们来跟踪算法进度并创建停止条件。我们通过仅使用195 MB的内存从增量4D-VAR的内环求解0.78 TB最小二乘子问题来证明算法的有效性。
As the scale of problems and data used for experimental design, signal processing and data assimilation grow, the oft-occuring least squares subproblems are correspondingly growing in size. As the scale of these least squares problems creates prohibitive memory movement costs for the usual incremental QR and Krylov-based algorithms, randomized least squares problems are garnering more attention. However, these randomized least squares solvers are difficult to integrate application algorithms as their uncertainty limits practical tracking of algorithmic progress and reliable stopping. Accordingly, in this work, we develop theoretically-rigorous, practical tools for quantifying the uncertainty of an important class of iterative randomized least squares algorithms, which we then use to track algorithmic progress and create a stopping condition. We demonstrate the effectiveness of our algorithm by solving a 0.78 TB least squares subproblem from the inner loop of incremental 4D-Var using only 195 MB of memory.
