2019/11/13 by Christopher Beattie, Zlatko Drmač, Beattie, C. +3 · 1 citation
Decision Sciences · Engineering · Physics and Astronomy · #Control Systems and Identification #FOS: Electrical engineering #FOS: Mathematics #Model Reduction and Neural Networks #Numerical Analysis (math.NA) #Probabilistic and Robust Engineering Design #Systems and Control (eess.SY) #electronic engineering #information engineering
paper · pdf · doi:10.48550/arxiv.1911.05804
openalex publication_date 2019/11/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The iterative rational Krylov algorithm (\textsfIRKA) is a popular approach for producing locally optimal reduced-order H2-approximations to linear time-invariant (LTI) dynamical systems. Overall, \textsfIRKA has seen significant practical success in computing high fidelity (locally) optimal reduced models and has been successfully applied in a variety of large-scale settings. Moreover, \textsfIRKA has provided a foundation for recent extensions to the systematic model reduction of bilinear and nonlinear dynamical systems. Convergence of the basic \textsfIRKA iteration is generally observed to be rapid --- but not always; and despite the simplicity of the iteration, its convergence behavior is remarkably complex and not well understood aside from a few special cases. The overall effectiveness and computational robustness of the basic \textsfIRKA iteration is surprising since its algorithmic goals are very similar to a pole assignment problem, which can be notoriously ill-conditioned. We investigate this connection here and discuss a variety of nice properties of the \textsfIRKA iteration that are revealed when the iteration is framed with respect to a primitive basis. We find that the connection with pole assignment suggests refinements to the basic algorithm that can improve convergence behavior, leading also to new choices for termination criteria that assure backward stability.