On the robustness of modified incomplete factorization methods

Abstract

We analyse the robustness of the (perturbed) modified incomplete factorization method. In the discrete PDE context, we show that, under very general assumptions, one may derive bounds which allow to prove convergence rates similar to those observed for model problems. Thus, contrarily to presently available results, we do not only give an idea of the efficiency of the method by proving the h ⁻¹-dependency of the associated spectral condition number, but also obtain explicit bounds that are sufficient by themselves to prove the robustness of the method. Further, our analysis is essentially based on theoretical arguments with rigorous proofs, which is a rather uncommon feature for a robustness study.

Keywords:

• Iterative methods for linear systems
• acceleration of convergence
• preconditioning

C.R. CATEGORIES::

• G1.3.G1.8.