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.
- Adi method
- Convergence of numerical methods
- Distributed-parameter systems
- Laplace transforms
- Lyapunov equation
ASJC Scopus subject areas
- Control and Systems Engineering