Deflated and Augmented Krylov Subspace Techniques

Andrew Chapman, Yousef Saad

Research output: Contribution to journalArticlepeer-review

132 Scopus citations


We present a general framework for a number of techniques based on projection methods on 'augmented Krylov subspaces'. These methods include the deflated GMRES algorithm, an inner-outer FGMRES iteration algorithm, and the class of block Krylov methods. Augmented Krylov subspace methods often show a significant improvement in convergence rate when compared with their standard counterparts using the subspaces of the same dimension. The methods can all be implemented with a variant of the FGMRES algorithm.

Original languageEnglish (US)
Pages (from-to)43-66
Number of pages24
JournalNumerical Linear Algebra with Applications
Issue number1
StatePublished - Jan 1 1997


  • Augmented Krylov subspace
  • Block GMRES
  • Deflated GMRES
  • Flexible GMRES
  • Inner-iteration GMRES


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