Consider the partitioning

The blockings of matrices *A* and *L* are identical.
Blocks and are scalars, and
are row vectors,
and and are column vectors. Sub-matrices
, , , and
are square matrices.

The assumption is that bold-face parts of the lower triangular
matrix have already been computed, and have overwritten the
corresponding parts of *A* . The rest of the matrix has not
been updated at all, and the object of the next step is
to compute the next parts of the lower triangular matrix,
and , overwriting the corresponding parts of
*A* .
From the above equation, we derive

Thus if and are to be updated by and , the following step will suffice:

The algorithm of left looking version of Cholesky factorization can be given as follows using the above equations

The PLAPACK implementation using global level-2 BLAS is given in Figure 8.3. In this code, at the top of the loop,

and `a_cur` the matrix