On the relations between ILUs and factored approximate inverses

Matthias Bollhöfer, Yousef Saad

Research output: Contribution to journalArticlepeer-review

32 Scopus citations


This paper discusses some relationships between ILU factorization techniques and factored sparse approximate inverse techniques. While ILU factorizations compute approximate LU factors of the coefficient matrix A, approximate inverse techniques aim at building triangular matrices Z and W such that WTAZ is approximately diagonal. The paper shows that certain forms of approximate inverse techniques amount to approximately inverting the triangular factors obtained from some variants of ILU faetorization of the original matrix. A few useful applications of these relationships will be discussed.

Original languageEnglish (US)
Pages (from-to)219-237
Number of pages19
JournalSIAM Journal on Matrix Analysis and Applications
Issue number1
StatePublished - 2003


  • ILU
  • Sparse approximate inverse
  • Sparse matrices
  • Variants of ILU


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