Preconditioners for Krylov subspace methods: an overview

John W. Pearson, Jennifer Pestana

Research output: Contribution to journalArticlepeer-review

21 Citations (Scopus)
151 Downloads (Pure)


When simulating a mechanism from science or engineering, or an industrial process, one is frequently required to construct a mathematical model, and then resolve this model numerically. If accurate numerical solutions are necessary or desirable, this can involve solving large-scale systems of equations. One major class of solution methods is that of preconditioned iterative methods, involving preconditioners which are computationally cheap to apply while also capturing information contained in the linear system. In this article, we give a short survey of the field of preconditioning. We introduce a range of preconditioners for partial differential equations, followed by optimization problems, before discussing preconditioners constructed with less standard objectives in mind.

Original languageEnglish
Article numbere202000015
Number of pages35
JournalGAMM-Mitteilungen / GAMM-Reports
Issue number4
Early online date21 Oct 2020
Publication statusPublished - 3 Nov 2020


  • preconditioning
  • iterative method
  • Krylov subspace method
  • partial differential equation
  • optimisation


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