4.1.3.3 Parallelization of $C_{n\times n} \;:=\; C_{n\times n} + A_{n\times n} \ast B_{n\times n}$

Starting point :

- outer product with rowise access
- Block matrices $C^{i,j}$, $A^{i,j}$, $B^{i,j}$
- 2D-Torus ( $n \times n$) Topology, distributed memory

     DO 
$k \;:=\; 1  ,  n$ 


DO 
$i \;:=\; 1  ,  n$ 


$C_{i,\ast} \;:=\; C_{i,\ast} + A_{i,k} \ast B_{k,\ast}$ 


END DO 


END DO 

The following algorithm was proposed by Fox [Fox88,KGGK94].



Remark : Finally, $\widetilde{B} \makebox[0pt]{}_{i,j} = B_{i,j}$ holds.