RSVDPACK：一种用于在多核和GPU架构上计算矩阵奇异值、插值和CUR分解的随机算法实现
RSVDPACK: An implementation of randomized algorithms for computing the singular value, interpolative, and CUR decompositions of matrices on multi-core and GPU architectures
AI总结：
RSVDPACK库通过高效随机算法实现矩阵低秩近似，支持SVD、ID和CUR分解，提升数据解释效率并降低内存需求。
摘要：
RSVDPACK是一个用于计算矩阵低秩近似的函数库，包含标准分解如奇异值分解（SVD）以及保持结构的分解如插值分解（ID）和CUR分解。ID和CUR分解通过选取矩阵的行/列子集作为行/列空间基，保留矩阵属性如稀疏性或非负性，有助于数据解释，并在某些情况下比部分SVD需要更少内存。该库基于随机采样实现高效算法，参考了Halko等人2011年的研究及后续论文。本文对基本算法进行了改进以提升性能和易用性，库采用C语言编写，支持多核CPU和GPU架构。
英文摘要：
RSVDPACK is a library of functions for computing low rank approximations of matrices. The library includes functions for computing standard (partial) factorizations such as the Singular Value Decomposition (SVD), and also so called "structure preserving" factorizations such as the Interpolative Decomposition (ID) and the CUR decomposition. The ID and CUR factorizations pick subsets of the rows/columns of a matrix to use as bases for its row/column space. Such factorizations preserve properties of the matrix such as sparsity or non-negativity, are helpful in data interpretation, and require in certain contexts less memory than a partial SVD. The package implements highly efficient computational algorithms based on randomized sampling, as described and analyzed in [N. Halko, P.G. Martinsson, J. Tropp, "Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions," SIAM Review, 53(2), 2011], and subsequent papers. This manuscript presents some modifications to the basic algorithms that improve performance and ease of use. The library is written in C and supports both multi-core CPU and GPU architectures.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
