  We show several ways to round a real matrix to an integer one such that the
rounding errors in all rows and columns as well as the whole matrix are less
than one. This is a classical problem with applications in many fields, in
particular, statistics.
  We improve earlier solutions of different authors in two ways. For rounding
matrices of size $m \times n$, we reduce the runtime from $O((m n)^2 Second,
our roundings also have a rounding error of less than one in all initial
intervals of rows and columns. Consequently, arbitrary intervals have an error
of at most two. This is particularly useful in the statistics application of
controlled rounding.
  The same result can be obtained via (dependent) randomized rounding. This has
the additional advantage that the rounding is unbiased, that is, for all
entries $y_{ij}$ of our rounding, we have $E(y_{ij}) = x_{ij}$, where $x_{ij}$
is the corresponding entry of the input matrix.
