English

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 H2\mathcal{H}_2 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 H2\mathcal{H}_2 approximation problem.

Keywords

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}
}
R2 v1 2026-06-21T18:42:43.046Z