A Stability Analysis of Incomplete LU Factorizations

TitleA Stability Analysis of Incomplete LU Factorizations
Publication TypeJournal Articles
Year of Publication1986
AuthorsElman H
JournalMathematics of Computation
Pagination191 - 217
Date Published1986/07/01/
ISBN Number0025-5718

The combination of iterative methods with preconditionings based on incomplete LU factorizations constitutes an effective class of methods for solving the sparse linear systems arising from the discretization of elliptic partial differential equations. In this paper, we show that there are some settings in which the incomplete LU preconditioners are not effective, and we demonstrate that their poor performance is due to numerical instability. Our analysis consists of an analytic and numerical study of a sample two-dimensional non-self-adjoint elliptic problem discretized by several finite-difference schemes.