Solve linear system with pre-calculated factorization

Hi,

I have a matrix A and I need to factorize this matrix every iteration. But I can decompose this matrix in this form:

A=BCD

Now just I need to factorize the matrix C every iteration instead of A (its 20 times faster to factorize C istead of A, because C is quasi-diagonal). And I can store the factorized terms of B and D and find the solution. But the solution using this is more costly, because I have to solve 3 systems now :

B = sparse(B);
C = sparse(C);
D = sparse(D);

[L1,U1,P1,Q1,R1] = lu(B);
[L4,U4,P4,Q4,R4] = lu(D);

% Inside of a loop1:
[L2,U2,P2,Q2,R2] = lu(C);
%loop2:
resp3=  Q2*(U2\(L2\(P2*(R2\Q4*(U4\(L4\(P4*(R4\Q1*(U1\(L1\(P1*(R1\b))))))))))));
%

This solution is more costly than factorize the whole matrix A and solve the system :

% Inside of a loop1 :
[L3,U3,P3,Q3,R3] = lu(A);
% Loop2:
resp = Q3*(U3\(L3\(P3*(R3\b))));
%

It is possible to use information of the matrix B and C to solve the linear system more efficiently than use the whole matrix A?