engleski

Numerical Implementation of the Iterative Rational Krylov Algorithm for Optimal H2 Model Reduction

The Iterative Rational Krylov (IRKA) algorithm for model order reduction (Gugercin, Antoulas, Beattie 2008.) has recently attracted attention because of its eff ectiveness in real world applications, as well as because of its mathematical elegance. Our goal is efficient and numerically reliable mathematical software that implements the IRKA algorithm. The first step is, necessarily, a theoretical study of the algorithm. We analyze the convergence of fixed point iterations, in particular the morphology of the key mapping ( fixed points, periodic points and their classification). Other theoretical issues include perturbation theory to analyze stability of the shifts, revealing relevant condition numbers, Cauchy{; ; ; like structure of certain key matrices, connection of the fixed point iterations and pole placement, proper stopping criterion that translates into a backward stability relation, etc.

model order reduction; rational Krylov algorithm

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