  The best column approximation in the Frobenius norm with $r$ columns has an
error at most $\sqrt{r+1}$ times larger than the truncated singular value
decomposition. Reaching this bound in practice involves either expensive random
volume sampling or at least $r$ executions of singular value decomposition. In
this paper it will be shown that the same column approximation bound can be
reached with only a single SVD (which can also be replaced with approximate
SVD). As a corollary, it will be shown how to find a highly nondegenerate
submatrix in $r$ rows of size $N$ in just $O(Nr^2)$ operations, which mostly
has the same properties as the maximum volume submatrix.
