A convergence rate for the ADI method for infinite-dimensional Lyapunov equations

Research output: Contribution to journalConference articlepeer-review


We show that the ADI method for a class of infinite-dimensional Lyapunov equations with appropriately chosen shift parameters converges exponentially in the square root. The main assumption on the class of Lyapunov equations is that the main operator generates an analytic semigroup. Rather than directly analyzing the ADI algorithm, we instead use that the ADI error is bounded by the error made by applying quadrature to the inverse Laplace transform integral of the output map and we analyze the error made by this quadrature approximation.
Original languageEnglish
Pages (from-to)373-377
Number of pages5
Issue number9
Early online date16 Jul 2021
Publication statusPublished - 16 Jul 2021

Bibliographical note

Publisher Copyright:
Copyright © 2021 The Authors. This is an open access article under the CC BY-NC-ND license.


  • Adi method
  • Convergence of numerical methods
  • Distributed-parameter systems
  • Laplace transforms
  • Lyapunov equation

ASJC Scopus subject areas

  • Control and Systems Engineering


Dive into the research topics of 'A convergence rate for the ADI method for infinite-dimensional Lyapunov equations'. Together they form a unique fingerprint.

Cite this