Accuracy and Numerical Stability Analysis of CUR Decompositions with Oversampling in Floating-Point Arithmetic

The CUR decomposition with cross approximation (CURCA), while computationally efficient, can be unstable due to the potential singularity of the core matrix. However, employing the epsilon-pseudoinverse and oversampling techniques can significantly enhance the numerical stability of CURCA, making it a viable option for low-rank matrix approximations even in the presence of rounding errors.