To derive a level-3 BLAS left-looking variant for computing the factorization, consider the partitioning

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

or

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

The PLAPACK implementation using global level-3 BLAS is given in Figure 8.4. This time the bulk of the computation is in the update , which is a matrix-panel operation. Thus, the algorithmic blocking size

PLA_Environ_nb_alg( PLA_OP_MAT_PAN, template, &nb_alg );

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