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All issues Volume 55 / No 2 (March-April 2021) ESAIM: M2AN, 55 2 (2021) 561-594 References
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Issue
ESAIM: M2AN
Volume 55, Number 2, March-April 2021
Page(s) 561 - 594
DOI https://doi.org/10.1051/m2an/2021001
Published online 31 March 2021
  1. A.C. Antoulas, Approximation of Large-Scale Dynamical Systems. In: Vol. 6 of Adv. Des. Control. SIAM Publications, Philadelphia, PA (2005). [Google Scholar]
  2. A.C. Antoulas and D.C. Sorensen, Approximation of large-scale dynamical systems: an overview. Int. J. Appl. Math. Comput. Sci. 11 (2001) 1093–1121. [Google Scholar]
  3. A.C. Antoulas, D.C. Sorensen and S. Gugercin, A survey of model reduction methods for large-scale systems. Contemp. Math. 280 (2001) 193–219. [Google Scholar]
  4. A.C. Antoulas, C.A. Beattie and S. Gugercin, Interpolatory model reduction of large-scale dynamical systems. In: Efficient Modeling and Control of Large-Scale Systems, edited by J. Mohammadpour and K.M. Grigoriadis. Springer US (2010) 3–58. [Google Scholar]
  5. A.C. Antoulas, C. Beattie and S. Gugercin, Interpolatory methods for model reduction. In: Vol. 6 of Computational Science and Engineering 21. Philadelphia, PA (2020). [Google Scholar]
  6. U. Baur, C.A. Beattie, P. Benner and S. Gugercin, Interpolatory projection methods for parameterized model reduction. SIAM J. Sci. Comput. 33 (2011) 2489–2518. [CrossRef] [Google Scholar]
  7. U. Baur, P. Benner and L. Feng, Model order reduction for linear and nonlinear systems: a system-theoretic perspective. Arch. Comput. Methods Eng. 21 (2014) 331–358. [Google Scholar]
  8. U. Baur, P. Benner, B. Haasdonk, C. Himpe, I. Martini and M. Ohlberger, Comparison of methods for parametric model order reduction of time-dependent problems. In: Model Reduction and Approximation: Theory and Algorithms, edited by P. Benner, A. Cohen, M. Ohlberger and K. Willcox. SIAM (2017) 377–407. [Google Scholar]
  9. P. Benner, M. Hinze and E.J.W. ter Maten, editors. Model reduction for circuit simulation. In: Vol. 74 of Lect. Notes Electr. Eng . Springer, Dodrecht (2011). [Google Scholar]
  10. P. Benner, S. Gugercin and K. Willcox, A survey of model reduction methods for parametric systems. SIAM Rev. 57 (2015) 483–531. [CrossRef] [Google Scholar]
  11. P. Benner, A. Cohen, M. Ohlberger and K. Willcox, editors. Model Reduction and Approximation: Theory and Algorithms. Computational Science & Engineering. SIAM Publications, Philadelphia, PA (2017). [Google Scholar]
  12. F. Chinesta, R. Keunings and A. Leygue, The Proper Generalized Decomposition for Advanced Numerical Simulations. SpringerBriefs in Applied Sciences and Technology. Springer International Publishing (2014). [Google Scholar]
  13. V. Druskin and V. Simoncini, Adaptive rational Krylov subspaces for large-scale dynamical systems. Syst. Control Lett. 60 (2011) 546–560. [Google Scholar]
  14. V. Druskin, V. Simoncini and M. Zaslavsky, Adaptive tangential interpolation in rational Krylov subspaces for MIMO dynamical systems. SIAM J. Matrix Anal. Appl. 35 (2014) 476–498. [Google Scholar]
  15. L. Feng and P. Benner, A robust algorithm for parametric model order reduction based on implicit moment matching, edited by A. Quarteroni and G. Rozza. In: Vol. 9 of Reduced Order Methods for Modeling and Computational Reduction, Chap. 6, MS&A Series. Springer-Verlag, Berlin, Heidelberg, NY (2014) 159–186. [Google Scholar]
  16. L. Feng and P. Benner, A new error estimator for reduce-order modeling of linear parametric systems. IEEE Trans. Microw. Theory Techn. 67 (2019) 4848–4859. [Google Scholar]
  17. L. Feng, A.C. Antoulas and P. Benner, Some a posteriori error bounds for reduced order modelling of (non-)parametrized linear systems. ESAIM: M2AN 51 (2017) 2127–2158. [EDP Sciences] [Google Scholar]
  18. G. Fotyga, M. Czarniewska, A. Lamecki and M. Mrozowski, Reliable greedy multipoint model-order reduction techniques for finite-element analysis. IEEE Trans. Antennas Propagat. 17 (2018) 821–824. [Google Scholar]
  19. A. Grimm, Parametric dynamical systems: Transient analysis and data driven modeling. Ph.D. thesis, Virginia Tech (2018). [Google Scholar]
  20. S. Hain, M. Ohlberger, M. Radic and K. Urban, A hierarchical a-posteriori error estimator for the reduced basis method. Cornell University. Preprint: arXiv:1802.03298 (2018). [Google Scholar]
  21. M.W. Hess, S. Grundel and P. Benner, Estimating the inf-sup constant in reduced basis methods for time-harmonic Maxwell’s equations. IEEE Trans. Microw. Theory Techn. 63 (2015) 3549–3557. [Google Scholar]
  22. J.S. Hesthaven, G. Rozza and B. Stamm, Certified Reduced Basis Methods for Parametrized Partial Differential Equations. SpringerBriefs in Mathematics. Springer, Cham (2016). [Google Scholar]
  23. M. Hund, P. Mlinarić and J. Saak, An H2⊗L2-optimal model order reduction approach for parametric linear time-invariant systems. Appl. Math. Mech. 18 (2018). [Google Scholar]
  24. D. Huynh, G. Rozza, S. Sen and A. Patera, A successive constraint linear optimization method for lower bounds of parametric coercivity and inf-sup lower bounds. C.R. Acad. Sci. Paris 345 (2007) 473–478. [Google Scholar]
  25. A. Monje-Real and V. de la Rubia, Electric field integral equation for fast frequency sweep for scattering of nonpenetrable objects via the reduced-basis method. IEEE Trans. Antennas Propagat. 68 (2020) 6232–6244. [Google Scholar]
  26. G. Rozza, D.B.P. Huynh and A.T. Patera, Reduced basis approximation and a posteriori error estimation for affinely parametrized elliptic coercive partial differential equations. Arch. Comput. Methods Eng. 15 (2008) 229–275. [Google Scholar]
  27. B. Salimbahrami, R. Eid and B. Lohmann, Model reduction by second order Krylov subspaces: extensions, stability and proportional damping. In: IEEE Conference on Computer Aided Control Systems Design. Springer International Publishing (2006) 2997–3002. [Google Scholar]
  28. A. Schmidt, D. Wittwar and B. Haasdonk, Rigorous and effective a-posteriori error bounds for nonlinear problems-application to RB methods. SimTech, University of Stuttgart (2018). [Google Scholar]
  29. K. Smetana, O. Zahm and A.T. Patera, Randomized residual-based error estimators for parametrized equations. SIAM J. Sci. Comput. 41 (2019) A900–A926. [Google Scholar]
  30. M. Yano, A space-time Petrov-Galerkin certified reduced basis method: application to the Boussinesq equations. SIAM J. Sci. Comput. 36 (2014) 232–266. [Google Scholar]
  31. Y. Zhang, L. Feng, S. Li and P. Benner, An efficient output error estimation for model order reduction of parametrized evolution equations. SIAM J. Sci. Comput. 37 (2015) B910–B936. [Google Scholar]

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