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

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

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
Title of host publicationIFAC PapersOnLine
Pages373
Number of pages5
Volume54
DOIs
Publication statusE-pub ahead of print - 16 Jul 2021

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