  The recently introduced algorithm randUTV provides a highly efficient
technique for computing accurate approximations to all the singular values of a
given matrix $A$. The original version of randUTV was designed to compute a
full factorization of the matrix in the form $A = UTV^*$ where $U$ and $V$ are
orthogonal matrices, and $T$ is upper triangular. The estimates to the singular
values of $A$ appear along the diagonal of $T$. This manuscript describes how
the randUTV algorithm can be modified when the only quantity of interest being
sought is the vector of approximate singular values. The resulting method is
particularly effective for computing the nuclear norm of $A$, or more
generally, other Schatten-$p$ norms. The report also describes how to compute
an estimate of the errors incurred, at essentially negligible cost.
