research

It turns out that several questions about IRKA remain unanswered for me theoretically. Therefore, starting with single-input, single-output linear dynamical systems, I want to write a detailed paper. If you are interested or have open questions about IRKA, let me know.

List of useful articles and books:

Balanced Truncation

• Sylvester, J. J. (1884). Sur l’équation en matrices \(px = xq\). Comptes Rendus de l’Académie des Sciences de Paris, 99, 67–71, 115–116.
• Gantmacher, F. R. (1959). The Theory of Matrices (Vol. 1). Chelsea Publishing Company.
• Kalman, R. E. (1960). On the general theory of control systems. IFAC Proceedings Volumes, 1(1), 491-502.
• Kalman, R. E., Falb, P. L., & Arbib, M. A. (1968). Topics in Mathematical System Theory. McGraw-Hill.
• Kalman, R. E. (1968). Lectures on Controllability and Observability.

Interpolatory Model Order Reduction

• Antoulas, A. C., Beattie, C. A., & Güğercin, S. (2020). Interpolatory Methods for Model Reduction. Society for Industrial and Applied Mathematics.