On truncated incomplete decompositions

Gabriel Wittum*, Frank Liebau

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


In the present paper we introduce truncated incomplete decompositions (TrILU) for constant coefficient matrices. This new ILU variant saves most of the memory and work usually needed to compute and store the factorization. Further it improves the smoothing and preconditioning properties of standard ILU-decompositions. Besides describing the algorithm, we give theoretical results concerning stability and convergence as well as the smoothing property and robustness for TrILU smoothing in a multi-grid method. Further, we add numerical results of TrILU as smoother in a multi-grid method and as preconditioner in a pcg-method fully confirming the theoretical results.

Original languageEnglish (US)
Pages (from-to)719-740
Number of pages22
JournalBIT Numerical Mathematics
Issue number4
StatePublished - Dec 1989
Externally publishedYes


  • AMS classification: 65N20
  • Incomplete decompositions
  • multi-grid method
  • preconditioning
  • robustness
  • smoothing
  • smoothing property

ASJC Scopus subject areas

  • Software
  • Computational Mathematics
  • Applied Mathematics
  • Computer Networks and Communications


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