Similarly, sparse submatrix-Cholesky can be expressed as follows.

In submatrix-Cholesky, as soon as column **k** has been computed, its
effects on all subsequent columns are computed immediately. Thus,
submatrix-Cholesky is sometimes said to be a `right-looking'
algorithm, since at each stage columns to the right of the current
column are modified. It can also be viewed as a `data-driven'
algorithm, since each new column is used as soon as it is completed to
make all modifications to all the subsequent columns it affects.
For this reason, Ortega [38] terms submatrix-Cholesky an
`immediate-update' algorithm. It is also sometimes referred to as a
`fan-out' algorithm, since the basic operation is for a single column
to affect multiple subsequent columns. We will see that these
characterizations of the column-Cholesky and submatrix-Cholesky
algorithms have important implications for parallel implementations.