# Question on ILU(0) Preconditioned GMRES

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 August 5, 2012, 14:21 Question on ILU(0) Preconditioned GMRES #1 Member   Shenren Xu Join Date: Jan 2011 Location: London, U.K. Posts: 64 Rep Power: 9 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

 August 6, 2012, 11:20 #2 Super Moderator     Praveen. C Join Date: Mar 2009 Location: Bangalore Posts: 284 Blog Entries: 6 Rep Power: 11 No, you never invert them. Since they are lower/upper matrices, you can solve using forward/backward substitution.

August 6, 2012, 19:19
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Shenren Xu
Join Date: Jan 2011
Location: London, U.K.
Posts: 64
Rep Power: 9
Quote:
 Originally Posted by praveen No, you never invert them. Since they are lower/upper matrices, you can solve using forward/backward substitution.

Thank you Praveen!

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