The Cholesy method
Starting point : K u = f
1. Decomposition algorithm (K = STS) taking into account the structure of the matrix K :
Computation for j = 2, 3, ..., N
If l0(j)+1 < j , computation for i = l0(j)+1, l0(j)+2, ..., j - 1 :
( l0(j) represents the row index for which, in the jth column, Kij = 0 for all i satisfying 0 < i < l0(j)+1 and Klo(j)+1, j <> 0 )
We then have the following system :
ST S u = f
And write :
ST y = f
with :
y = S u
The system is solved with a forward substitution :
2. Algorithm of the forward substitution :
The system S u = y is then solved using a backward substitution :
3. Algorithm of the backward substitution :