A stability analysis of incomplete LU factorizations
Mathematics of Computation
Hybrid Krylov methods for nonlinear systems of equations
SIAM Journal on Scientific and Statistical Computing
A flexible inner-outer preconditioned GMRES algorithm
SIAM Journal on Scientific Computing
A Restarted GMRES Method Augmented with Eigenvectors
SIAM Journal on Matrix Analysis and Applications
Experimental study of ILU preconditioners for indefinite matrices
Journal of Computational and Applied Mathematics
The symmetric eigenvalue problem
The symmetric eigenvalue problem
Approximate Inverse Preconditioners via Sparse-Sparse Iterations
SIAM Journal on Scientific Computing
Iterative Methods for Sparse Linear Systems
Iterative Methods for Sparse Linear Systems
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This paper presents a class of preconditioning techniques which exploit rational function approximations to the inverse of the original matrix. The matrix is first shifted and then an incomplete LU factorization of the resulting matrix is computed. The resulting factors are then used to compute a better preconditioner for the original matrix. Since the incomplete factorization is made on a shifted matrix, a good LU factorization is obtained without allowing much fill-in. The result needs to be extrapolated to the nonshifted matrix. Thus, the main motivation for this process is to save memory. The method is useful for matrices whose incomplete LU factorizations are poor, e.g., unstable.