  This work investigates the accuracy and numerical stability of CUR
decompositions with oversampling. The CUR decomposition approximates a matrix
using a subset of columns and rows of the matrix. When the number of columns
and the rows are the same, the CUR decomposition can become unstable and less
accurate due to the presence of the matrix inverse in the core matrix.
Nevertheless, we demonstrate that the CUR decomposition can be implemented in a
numerical stable manner and illustrate that oversampling, which increases
either the number of columns or rows in the CUR decomposition, can enhance its
accuracy and stability. Additionally, this work devises an algorithm for
oversampling motivated by the theory of the CUR decomposition and the
cosine-sine decomposition, whose competitiveness is illustrated through
experiments.
