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 :