  A technique for computing an ILU preconditioner based on the FAPINV algorithm
is presented. We show that this algorithm is well-defined for H-matrices.
Moreover, when used in conjunction with Krylov-subspace-based iterative solvers
such as the GMRES algorithm, results in reliable solvers. Numerical experiments
on some test matrices are given to show the efficiency of the new ILU
preconditioner.
