ADI iteration for Lyapunov equations: A tangential approach and adaptive shift selection

Thomas Wolf, Heiko K.F. Panzer, Boris Lohmann

Research output: Contribution to journalArticlepeer-review

5 Scopus citations

Abstract

A new version of the alternating directions implicit (ADI) iteration for the solution of large-scale Lyapunov equations is introduced. It generalizes the hitherto existing iteration, by incorporating tangential directions in the way they are already available for rational Krylov subspaces. Additionally, first strategies to adaptively select shifts and tangential directions in each iteration are presented. Numerical examples emphasize the potential of the new results.

Original languageEnglish
Pages (from-to)85-95
Number of pages11
JournalApplied Numerical Mathematics
Volume109
DOIs
StatePublished - 1 Nov 2016

Keywords

  • ADI iteration
  • Large-scale systems
  • Lyapunov equation

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