The Loewner framework and transfer functions of singular/rectangular systems. A connection is established between the Loewner framework for model reduction and the generalized inverses of singular and rectangular matrices. In this context both the Moore-Penrose and the Drazin inverses are involved. As a consequence this approach yields transfer functions for singular and rectangular systems. Thus the Loewner framework constitutes a natural and direct way for constructing models from measured input/output data.

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  1. Benner, Peter; Goyal, Pawan: Interpolation-based model order reduction for polynomial systems (2021)
  2. Brevis, Ignacio; Muga, Ignacio; van der Zee, Kristoffer G.: A machine-learning minimal-residual (ML-MRes) framework for goal-oriented finite element discretizations (2021)
  3. Haasdonk, Bernard: MOR software (2021)
  4. Antoulas, Athanasios C.; Gosea, Ion Victor; Heinkenschloss, Matthias: Data-driven model reduction for a class of semi-explicit DAEs using the Loewner framework (2020)
  5. Beattie, Christopher; Gugercin, Serkan; Tomljanović, Zoran: Sampling-free model reduction of systems with low-rank parameterization (2020)
  6. Benner, Peter; Goyal, Pawan; Kramer, Boris; Peherstorfer, Benjamin; Willcox, Karen: Operator inference for non-intrusive model reduction of systems with non-polynomial nonlinear terms (2020)
  7. Gosea, Ion Victor; Duff, Igor Pontes; Benner, Peter; Antoulas, Athanasios C.: Model order reduction of switched linear systems with constrained switching (2020)
  8. Gosea, Ion Victor; Zhang, Qiang; Antoulas, Athanasios C.: Preserving the DAE structure in the Loewner model reduction and identification framework (2020)
  9. Hijazi, Saddam; Stabile, Giovanni; Mola, Andrea; Rozza, Gianluigi: Data-driven POD-Galerkin reduced order model for turbulent flows (2020)
  10. Kergus, Pauline; Demourant, Fabrice; Poussot-Vassal, Charles: Identification of parametric models in the frequency-domain through the subspace framework under LMI constraints (2020)
  11. Nakatsukasa, Yuji; Trefethen, Lloyd N.: An algorithm for real and complex rational minimax approximation (2020)
  12. Peherstorfer, Benjamin: Sampling low-dimensional Markovian dynamics for preasymptotically recovering reduced models from data with operator inference (2020)
  13. Pradovera, Davide: Interpolatory rational model order reduction of parametric problems lacking uniform inf-sup stability (2020)
  14. Regazzoni, F.; Dedè, L.; Quarteroni, A.: Machine learning of multiscale active force generation models for the efficient simulation of cardiac electromechanics (2020)
  15. Scarciotti, Giordano; Jiang, Zhong-Ping; Astolfi, Alessandro: Data-driven constrained optimal model reduction (2020)
  16. Rapisarda, P.: Discrete Roesser state models from 2D frequency data (2019)
  17. Regazzoni, F.; Dedè, L.; Quarteroni, A.: Machine learning for fast and reliable solution of time-dependent differential equations (2019)
  18. Carracedo Rodriguez, Andrea; Gugercin, Serkan; Borggaard, Jeff: Interpolatory model reduction of parameterized bilinear dynamical systems (2018)
  19. Gosea, I. V.; Petreczky, M.; Antoulas, A. C.: Data-driven model order reduction of linear switched systems in the Loewner framework (2018)
  20. Schulze, Philipp; Unger, Benjamin; Beattie, Christopher; Gugercin, Serkan: Data-driven structured realization (2018)

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