论文标题
使用有效的采样和迭代技术进行奇异值分解的快速准确的正交分解
Fast and Accurate Proper Orthogonal Decomposition using Efficient Sampling and Iterative Techniques for Singular Value Decomposition
论文作者
论文摘要
在本文中，我们建议使用基于随机抽样的技术进行适当正交分解（POD）的计算有效迭代算法。在此算法中，采样了其他行和列，并使用合并技术来更新每次迭代中的主要POD模式。我们得出了一系列合并操作引入的误差的光谱规范的界限。我们使用现有定理来大致衡量在迭代收敛时获得的子空间质量。各种数据集上的结果表明，与计算截断的SVD相比，POD模式和/或子空间的近似精度具有出色的精度。我们还提出了一种使用这种迭代采样和合并算法来计算不适合RAM的大型矩阵的POD模式的方法。
In this paper, we propose a computationally efficient iterative algorithm for proper orthogonal decomposition (POD) using random sampling based techniques. In this algorithm, additional rows and columns are sampled and a merging technique is used to update the dominant POD modes in each iteration. We derive bounds for the spectral norm of the error introduced by a series of merging operations. We use an existing theorem to get an approximate measure of the quality of subspaces obtained on convergence of the iteration. Results on various datasets indicate that the POD modes and/or the subspaces are approximated with excellent accuracy with a significant runtime improvement over computing the truncated SVD. We also propose a method to compute the POD modes of large matrices that do not fit in the RAM using this iterative sampling and merging algorithms.
