Convergence of the Iterative Rational Krylov Algorithm
Numerical Analysis
2013-01-23 v1
Abstract
The Iterative Rational Krylov Algorithm (IRKA) of [8] is an interpolatory model reduction approach to the optimal approximation problem. Even though the method has been illustrated to show rapid convergence in various examples, a proof of convergence has not been provided yet. In this note, we show that in the case of state-space symmetric systems, IRKA is a locally convergent fixed point iteration to a local minimum of the underlying approximation problem.
Cite
@article{arxiv.1107.5363,
title = {Convergence of the Iterative Rational Krylov Algorithm},
author = {Garret Flagg and Christopher Beattie and Serkan Gugercin},
journal= {arXiv preprint arXiv:1107.5363},
year = {2013}
}