Grout versions of ILU for general sparse matrices

Na Li, Yousef Saad, Edmond Chow

Research output: Contribution to journalArticlepeer-review

87 Scopus citations


This paper presents an efficient implementation of the incomplete LU (ILU) factorization derived from the Croat version of Gaussian elimination. At step k of the elimination, the kth row of U and the kth column of L are computed using previously computed rows of U and columns of L. The data structure and implementation borrow from already known techniques used in developing both sparse direct solution codes and incomplete Cholesky factorizations. This version of ILU can be computed much faster than standard threshold-based ILU factorizations computed rowwise or columnwise. In addition, the data structure allows efficient implementations of more rigorous and effective dropping strategies.

Original languageEnglish (US)
Pages (from-to)716-728
Number of pages13
JournalSIAM Journal on Scientific Computing
Issue number2
StatePublished - Nov 2003


  • Crout factorization
  • ILU
  • ILU with threshold
  • ILUT
  • Incomplete LU factorization
  • Iterative methods
  • Preconditioning
  • Sparse Gaussian elimination
  • Sparse linear systems


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