论文标题
低级别近似的单通行随机QLP分解
Single-pass randomized QLP decomposition for low-rank approximation
论文作者
论文摘要
QLP分解是在数值线性代数中近似奇异值分解（SVD）的有效算法之一。在本文中，我们提出了一些用于计算低级数矩阵近似的单通行QLP分解算法。与确定性QLP分解相比，所提出的算法的复杂性并未显着增加，并且仅访问一次系统矩阵。因此，我们的算法非常适合存储在内存外或流数据生成的大型矩阵。在错误分析中，我们给出矩阵近似误差和单数值近似误差的边界。数值实验还报告了验证我们的结果。
The QLP decomposition is one of the effective algorithms to approximate singular value decomposition (SVD) in numerical linear algebra. In this paper, we propose some single-pass randomized QLP decomposition algorithms for computing the low-rank matrix approximation. Compared with the deterministic QLP decomposition, the complexity of the proposed algorithms does not increase significantly and the system matrix needs to be accessed only once. Therefore, our algorithms are very suitable for a large matrix stored outside of memory or generated by stream data. In the error analysis, we give the bounds of matrix approximation error and singular value approximation error. Numerical experiments also reported to verify our results.
