Question on ILU(0) Preconditioned GMRES
 

Dear colleagues,

I have a few questions concerning using ILU(0) for preconditioning the GMRES solver.

As far as I know, ILU(0) decomposes my original system matrix A into

A=L*U+R

where L and R are lower and upper triangular matrices with the same non-zero pattern as my sparse matrix A.

The original linear system

A *x = b

is then preconditioned as

A_new * x = b_new

where A_new=inv(U)*inv(L)*A and b_new = inv(U)*inv(L)*b. The new linear system is solved using GMRES.

My questions are

1) Do I need to explicitly invert L and U? If yes, how do I invert these sparse matrix? Wouldn't the non-zero pattern be destroyed then?

2) In matlab gmres code, one calls it with gmres(... A,..., L,U,...), i.e., only L and U are needed. Then how does matlab invert them, if ever?

3) Anyone has experience on using LASPACK's ILU preconditioned GMRES? Looks like it's ILU is only implemented for symmetric matrix.

Regards,
Shenren

No, you never invert them. Since they are lower/upper matrices, you can solve using forward/backward substitution.

Thank you Praveen!