In this work, we analyze a sublinear-time algorithm for selecting a few rows and columns of a matrix for low-rank approximation purposes. The algorithm is based on an initial uniformly random selection of rows and columns, followed by a refinement of this choice using a strong rank-revealing QR factorization. We prove bounds on the error of the corresponding low-rank approximation (more precisely, the CUR approximation error) when the matrix is a perturbation of a low-rank matrix that can be factorized into the product of matrices with suitable incoherence and/or sparsity assumptions.

翻译：本文分析了一种用于矩阵低秩近似的行与列子集选择的次线性时间算法。该算法首先均匀随机选取初始行与列，随后通过强秩揭示QR分解对选取结果进行优化。当矩阵为可分解为满足适当不相关性及/或稀疏性假设的矩阵乘积的低秩矩阵的扰动时，我们证明了相应低秩近似（更精确地说，CUR近似误差）的误差界。