Perturbations of CUR Decompositions

The CUR decomposition is a factorization of low-rank matrix obtained by selecting certain column and row submatrices it. We perform thorough investigation what happens to such decompositions in the presence noise. Since are nonuniquely formed, we investigate several variants give perturbation estimates for each terms magnitude noise broad class norms which includes all Schatten $p$-norms. given here qualitative illustrate how choice columns rows affects quality approximation, additionally obtain new state-of-the-art bounds some approximations.