On the stability of relaxed incomplete 𝐿𝑈 factorizations

Bruaset, A. M.; Tveito, A.; Winther, R.

doi:10.1090/S0025-5718-1990-0993924-X

On the stability of relaxed incomplete $LU$ factorizations
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by A. M. Bruaset, A. Tveito and R. Winther PDF

Math. Comp. 54 (1990), 701-719 Request permission

Abstract:

When solving large linear systems of equations arising from the discretization of elliptic boundary value problems, a combination of iterative methods and preconditioners based on incomplete LU factorizations is frequently used. Given a model problem with variable coefficients, we investigate a class of incomplete LU factorizations depending on a relaxation parameter. We show that the associated preconditioner and the factorization itself both are numerically stable. The theoretical results are complemented by numerical experiments.

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