PMTBR: A family of approximate principal-components-like reduction algorithms We present a family of algorithms that can be considered intermediate between frequency domain projection methods and approximation of truncated balanced realizations. The methods discussed are computationally simple to implement, have good error properties, and possess simple error estimation and order control procedures. By tailoring the method to take into account a statistical representation of individual problem characteristics, more efficient, improved results have been obtained in several situations, meaning models of small order that retain acceptable accuracy, on problems for which many other methods struggle. Examples are shown to illustrate the algorithms in the contexts of frequency weighting, circuit simulation with parasitics networks having large numbers of input/output ports, and interconnect modeling in the presence of parameter change due to process variation.

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  1. Gosea, Ion Victor; Gugercin, Serkan; Beattie, Christopher: Data-driven balancing of linear dynamical systems (2022)
  2. Nouri, Behzad; Gad, Emad; Nakhla, Michel; Achar, Ram: Model order reduction in microelectronics (2021)
  3. Wang, Xinsheng; Yu, Mingyan; Wang, Chenxu: Structure-preserving-based model-order reduction of parameterized interconnect systems (2018)
  4. Yang, Jun-Man; Jiang, Yao-Lin: Krylov subspace approximation for quadratic-bilinear differential system (2018)
  5. Benner, Peter; Stykel, Tatjana: Model order reduction for differential-algebraic equations: a survey (2017)
  6. Breiten, Tobias: Structure-preserving model reduction for integro-differential equations (2016)
  7. Mohaghegh, Kasra; Pulch, Roland; ter Maten, Jan: Model order reduction using singularly perturbed systems (2016)
  8. Baur, Ulrike; Benner, Peter; Feng, Lihong: Model order reduction for linear and nonlinear systems: a system-theoretic perspective (2014)
  9. Burgard, Stefan; Farle, Ortwin; Dyczij-Edlinger, Romanus: A novel parametric model order reduction approach with applications to geometrically parameterized microwave devices (2013)
  10. Fehr, Jörg; Fischer, Michael; Haasdonk, Bernard; Eberhard, Peter: Greedy-based approximation of frequency-weighted Gramian matrices for model reduction in multibody dynamics (2013)
  11. Baur, Ulrike; Beattie, Christopher; Benner, Peter; Gugercin, Serkan: Interpolatory projection methods for parameterized model reduction (2011)
  12. Ferranti, Francesco; Antonini, Giulio; Dhaene, Tom; Knockaert, Luc: Passivity-preserving interpolation-based parameterized model order reduction of PEEC models based on scattered grids (2011)
  13. Rommes, Joost; Martins, Nelson: Exploiting structure in large-scale electrical circuit and power system problems (2009)
  14. Verhoeven, Arie; Maten, Jan Ter; Striebel, Michael; Mattheij, Robert: Model order reduction for nonlinear IC models (2009)
  15. Phillips, Joel R.; Zhu, Zhenhai; Siveira, Miguel: PMTBR: A family of approximate principal-components-like reduction algorithms (2008)
  16. Voss, Thomas; Verhoeven, Arie; Bechtold, Tamara; ter Maten, Jan: Model order reduction for nonlinear differential algebraic equations in circuit simulation (2008)
  17. Ionutiu, Roxana; Lefteriu, Sanda; Antoulas, Athanasios C.: Comparison of model reduction methods with applications to circuit simulation (2007)
  18. Silva, João M. S.; Villena, Jorge Fernández; Flores, Paulo; Silveira, L. Miguel: Outstanding issues in model order reduction (2007)
  19. Voß, T.; Pulch, R.; ter Maten, E. J. W.; El Guennouni, A.: Trajectory piecewise linear approach for nonlinear differential-algebraic equations in circuit simulation (2007)
  20. Phillips, Joel R.; Silveira, Luis Miguel: Poor man’s TBR: a simple model reduction scheme. (2005) ioport