Factorized sparse approximate inverses for preconditioning

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Abstract

In recent papers the use of sparse approximate inverses for the preconditioning of linear equations Ax = b is examined. The minimization of ||AM - I|| in the Frobenius norm generates good preconditioners without any a priori knowledge on the pattern of M. For symmetric positive definite A and a given a priori pattern there exist methods for computing factorized sparse approximate inverses L with LLT ≈ A-1. Here, we want to modify these algorithms that they are able to capture automatically a promising pattern for L.We use these approximate inverses for solving linear equations with the cg-method. Furthermore we introduce and test modifications of this method for computing factorized sparse approximate inverses.

Original languageEnglish
Pages (from-to)109-117
Number of pages9
JournalJournal of Supercomputing
Volume25
Issue number2
DOIs
StatePublished - Jun 2003

Keywords

  • Factorized sparse approximate inverse
  • Preconditioned conjugate gradients
  • Sparse linear systems

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