Multigrid treatment and robustness enhancement for factored sparse approximate inverse preconditioning

Kai Wang, Jun Zhang

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


We investigate the use of sparse approximate inverse techniques (SAI) in a grid based multilevel ILU preconditioner (GILUM) to design a robust and parallelizable preconditioner for solving general sparse matrices. Taking the advantages of grid based multilevel methods, the resulting preconditioner outperforms sparse approximate inverse in robustness and efficiency. Conversely, taking the advantages of sparse approximate inverse, it affords an easy and convenient way to introduce parallelism within multilevel structure. Moreover, an independent set search strategy with automatic diagonal thresholding and a relative threshold dropping strategy are proposed to improve preconditioner performance. Numerical experiments are used to show the effectiveness and efficiency of the proposed preconditioner, and to compare it with some single and multilevel preconditioners.

Original languageEnglish
Pages (from-to)483-500
Number of pages18
JournalApplied Numerical Mathematics
Issue number4
StatePublished - Dec 2002

Bibliographical note

Funding Information:
✩ This research was supported in part by the US National Science Foundation under grants CCR-9902022, CCR-9988165, and CCR-0092532. * Corresponding author. E-mail addresses: (K. Wang), (J. Zhang). URL address:


  • Algebraic multigrid method
  • Incomplete LU factorization
  • Krylov subspace methods
  • Multilevel ILU preconditioner
  • Sparse approximate inverse
  • Sparse matrices

ASJC Scopus subject areas

  • Numerical Analysis
  • Computational Mathematics
  • Applied Mathematics


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