Modification and compensation strategies for threshold-based incomplete factorizations

S. MacLachlan, D. Osei-Kuffuor, Yousef Saad

Research output: Contribution to journalArticlepeer-review

9 Scopus citations

Abstract

Standard (single-level) incomplete factorization preconditioners are known to successfully accelerate Krylov subspace iterations for many linear systems. The classical modified incomplete LU (MILU) factorization approach improves the acceleration given by (standard) ILU approaches, by modifying the nonunit diagonal in the factorization to match the action of the system matrix on a given vector, typically the constant vector. Here, we examine the role of similar modifications within the dual-threshold ILUT algorithm. We introduce column and row variants of the modified ILUT algorithm and discuss optimal ways of modifying the columns or rows of the computed factors to improve their accuracy and stability. Modifications are considered for both the diagonal and offdiagonal entries of the factors, based on one or many vectors, chosen a priori or through an Arnoldi iteration. Numerical results are presented to support our findings.

Original languageEnglish (US)
Pages (from-to)A48-A75
JournalSIAM Journal on Scientific Computing
Volume34
Issue number1
DOIs
StatePublished - May 28 2012

Keywords

  • Algebraic preconditioners
  • ILUT
  • Incomplete factorization preconditioners
  • Modified ILU

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