Multilevel preconditioners constructed from inverse-based ILUs

Matthias Bollhöfer, Yousef Saad

Research output: Contribution to journalArticlepeer-review

109 Scopus citations


This paper analyzes dropping strategies in a multilevel incomplete LU decomposition context and presents a few strategies for obtaining related ILUs with enhanced robustness. The analysis shows that the incomplete LU factorization resulting from dropping small entries in Gaussian elimination produces a good preconditioner when the inverses of these factors have norms that are not too large. As a consequence a few strategies are developed whose goal is to achieve this feature. A number of "templates" for enabling implementations of these factorizations are presented. Numerical experiments show that the resulting ILUs offer a good compromise between robustness and efficiency.

Original languageEnglish (US)
Pages (from-to)1627-1650
Number of pages24
JournalSIAM Journal on Scientific Computing
Issue number5
StatePublished - 2006


  • Algebraic multilevel method
  • Approximate inverse
  • ILU
  • Incomplete LU decompositions
  • Iterative solver
  • Multilevel ILU
  • Preconditioning


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