1)

L = A;

2)

for i = 1, number_of_tree_nodes do

3)

= node of tree;

4)

for all child of do

5)

prepare update of by j-th child;

6)

atomic;

7)

end

8)

Calculate LL^T decomposition of;

9)

end

10)

parallel for j = 1, number_of_tree_node do

11)

prepare update of Z_C by j-th child;

12)

atomic;

13)

end