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Incomplete Factorization Preconditioners

A broad class of preconditioners is based on incomplete factorizations of the coefficient matrix. We call a factorization incomplete if during the factorization process certain fill elements, zero positions that would be nonzero in an exact factorization, have been ignored. Such a preconditioner is then given in factored form with lower and upper triangular. The efficacy of the preconditioner depends on how well approximates .

• Creating an incomplete factorization
• Point incomplete factorizations
  • Special cases: central differences
  • Modified incomplete factorizations
  • Parallelism aspects
• Block factorization methods
  • The idea behind block factorizations
  • Approximate inverses
  • The special case of block tridiagonality
  • Two types of incomplete block factorizations
  • Blocking over systems of partial differential equations
• Incomplete LQ factorizations