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On the stability of the incomplete Cholesky decomposition for a singular perturbed problem, where the coefficient matrix is not an \(M\)-matrix. (English) Zbl 0826.65101

The incomplete Cholesky decomposition is known to provide good smoothers in multigrid algorithms. These smoothers are of special interest for problems with singular perturbations since they can often compensate the poorer approximation of the coarse grid correction. On the other hand singular perturbations often imply that the matrices are no longer \(M\)- matrices.
In this paper the stability of a modified ILU-decomposition is shown for a problem in which the singular perturbation arises from an anisotropy.
Reviewer: D.Braess (Bochum)

MSC:

65N55 Multigrid methods; domain decomposition for boundary value problems involving PDEs
65N12 Stability and convergence of numerical methods for boundary value problems involving PDEs
65F10 Iterative numerical methods for linear systems
35B25 Singular perturbations in context of PDEs
35J25 Boundary value problems for second-order elliptic equations
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