In Section 1.2,
we gave the following description for the Cholesky factorization
of matrix *A*:

where and are scalars and
and are vectors of length *n*-1 .
The indicates the symmetric part of *A* .
Now,

This in turn yields the equations

We conclude that the following steps will implement the
Cholesky factorization, overwriting the lower triangular
portion of *A* with *L* :

- compute the Cholesky factorization of updated recursively, yielding .

Given the PLAPACK level-1 and level-2 BLAS operations described in
previous chapters, a complete implementation
is given in
Figure 8.1.
In this implementation, the ``current'' matrix *A* is
referenced by `acur`. The routine `Take_sqrt`
overwrites the view of sub-matrix by
its square-root. The comments to the right of the algorithm
give essentially the description of the algorithm as
presented in the text. Notice that indeed the code is
line-for-line a translation of this algorithm.