Experimental study of ILU preconditioners for indefinite matrices

Edmond Chow, Yousef Saad

Research output: Contribution to journalArticlepeer-review

182 Scopus citations


Incomplete LU factorization preconditioners have been surprisingly successful for many cases of general nonsymmetric and indefinite matrices. However, their failure rate is still too high for them to be useful as black-box library software for general matrices. Besides fatal breakdowns due to zero pivots, the major causes of failure are inaccuracy, and instability of the triangular solves. When there are small pivots, both these problems can occur, but these problems can also occur without small pivots. Through examples from actual problems, this paper shows how these problems evince themselves, how these problems can be detected, and how these problems can sometimes be circumvented through pivoting, reordering, scaling, perturbing diagonal elements, and preserving symmetric structure. The goal of this paper is to gain a better practical understanding of ILU preconditioners and help improve their reliability.

Original languageEnglish (US)
Pages (from-to)387-414
Number of pages28
JournalJournal of Computational and Applied Mathematics
Issue number2
StatePublished - Dec 10 1997

Bibliographical note

Funding Information:
* Corresponding author. E-mail: chow@cs.umn.edu ~Work supported in part by the National Science Foundation under grant NSF/CCR-9618827 and in part by NASA under grant NAG2-904.


  • Incomplete factorization preconditioning
  • Instability
  • Ordering
  • Pivoting


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