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 nonzero 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 nonzero 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.

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Thank you Praveen! 
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