Bibliography¶
Eman Salem Al-Aidarous. Symplectic gram-schmidt algorithm with re-orthogonalization. Journal of King Abdulaziz University: Science, 23(1):11–20, 2011. doi:10.4197/Sci.23-1.2.
A. C. Antoulas. Approximation of Large-Scale Dynamical Systems. Volume 6 of Adv. Des. Control. SIAM Publications, Philadelphia, PA, 2005. ISBN 9780898715293. doi:10.1137/1.9780898718713.
A. C. Antoulas, C. A. Beattie, and S. Gugercin. Interpolatory model reduction of large-scale dynamical systems. In Javad Mohammadpour and Karolos M. Grigoriadis, editors, Efficient Modeling and Control of Large-Scale Systems, pages 3–58. Springer US, 2010. doi:10.1007/978-1-4419-5757-3_1.
S. Barrachina, P. Benner, and E. S. Quintana-Ortí. Efficient algorithms for generalized algebraic Bernoulli equations based on the matrix sign function. Numer. Algorithms, 46(4):351–368, 2007. doi:10.1007/s11075-007-9143-x.
C. A. Beattie and S. Gugercin. Interpolatory projection methods for structure-preserving model reduction. Systems Control Lett., 58(3):225–232, 2009. doi:10.1016/j.sysconle.2008.10.016.
C. A. Beattie and S. Gugercin. Realization-independent $\mathcal H_2$-approximation. In 51st IEEE Conference on Decision and Control (CDC), 4953–4958. 2012. doi:10.1109/CDC.2012.6426344.
P. Benner, M. Köhler, and J. Saak. Sparse-dense Sylvester equations in $H_2$-model order reduction. Preprint MPIMD/11-11, Max Planck Institute Magdeburg, December 2011. URL: https://csc.mpi-magdeburg.mpg.de/preprints/2011/11/.
Peter Benner, Zvonimir Bujanović, Patrick Kürschner, and Jens Saak. Radi: a low-rank adi-type algorithm for large scale algebraic riccati equations. Numerische mathematik, 138(2):301–330, 2018.
Peter Binev, Albert Cohen, Wolfgang Dahmen, Ronald DeVore, Guergana Petrova, and Przemyslaw Wojtaszczyk. Convergence rates for greedy algorithms in reduced basis methods. SIAM journal on mathematical analysis, 43(3):1457–1472, 2011.
Tobias Breiten, Chris A. Beattie, and Serkan Gugercin. $\mathcal H_2$-gap model reduction for stabilizable and detectable systems. e-prints 1909.13764, arXiv, 2019. math.NA. URL: http://arxiv.org/abs/1909.13764.
Patrick Buchfink, Ashish Bhatt, and Bernard Haasdonk. Symplectic model order reduction with non-orthonormal bases. Mathematical and Computational Applications, 2019. doi:10.3390/mca24020043.
Andreas Buhr, Christian Engwer, Mario Ohlberger, and Stephan Rave. A numerically stable a posteriori error estimator for reduced basis approximations of elliptic equations. arXiv preprint arXiv:1407.8005, 2014.
Andreas Buhr and Kathrin Smetana. Randomized local model order reduction. SIAM journal on scientific computing, 40(4):A2120–A2151, 2018.
Y. Chahlaoui, D. Lemonnier, A. Vandendorpe, and P. Van Dooren. Second-order balanced truncation. Linear Algebra Appl., 415(2–3):373–384, 2006. doi:10.1016/j.laa.2004.03.032.
B. Clapperton, F. Crusca, and M. Aldeen. Bilinear transformation and generalized singular perturbation model reduction. IEEE Transactions on Automatic Control, 41(4):589–593, 1996. doi:10.1109/9.489281.
Martin A Grepl and Anthony T Patera. A posteriori error bounds for reduced-basis approximations of parametrized parabolic partial differential equations. ESAIM: Mathematical Modelling and Numerical Analysis, 39(1):157–181, 2005.
S. Gugercin, A. C. Antoulas, and C. Beattie. $\mathcal H_2$ model reduction for large-scale linear dynamical systems. SIAM J. Matrix Anal. Appl., 30(2):609–638, 2008. doi:10.1137/060666123.
B. Haasdonk. Reduced basis methods for parametrized PDEs—a tutorial introduction for stationary and instationary problems. In P. Benner, A. Cohen, M. Ohlberger, and K. Willcox, editors, Model Reduction and Approximation: Theory and Algorithms, pages 65–136. SIAM, 2017. doi:10.1137/1.9781611974829.ch2.
B. Haasdonk, M. Dihlmann, and M. Ohlberger. A training set and multiple basis generation approach for parametrized model reduction based on adaptive grids in parameter space. Math. Comput. Model. Dyn. Syst., 17(4):423–442, 2011.
B. Haasdonk and M. Ohlberger. Reduced basis method for finite volume approximations of parametrized linear evolution equations. ESAIM: Math. Model. Numer. Anal., 42(2):277–302, 2008.
Jan S Hesthaven and Stefano Ubbiali. Non-intrusive reduced order modeling of nonlinear problems using neural networks. Journal of Computational Physics, 363:55–78, 2018.
C. Himpe, T. Leibner, and S. Rave. Hierarchical approximate proper orthogonal decomposition. SIAM J. Sci. Comput., 40(5):A3267–A3292, 2018. doi:10.1137/16M1085413.
Michael Hinze, René Pinnau, Michael Ulbrich, and Stefan Ulbrich. Optimization with PDE constraints. Volume 23. Springer Science & Business Media, 2008.
Patrick Kürschner. Efficient low-rank solution of large-scale matrix equations. PhD thesis, Shaker Verlag Aachen, 2016. URL: http://pubman.mpdl.mpg.de/pubman/.
Richard Bruno Lehoucq. Analysis and implementation of an implicitly restarted Arnoldi iteration. PhD thesis, Rice University, Houston, USA, 1995. URL: https://scholarship.rice.edu/handle/1911/16844.
J.-R. Li and J. White. Low rank solution of Lyapunov equations. SIAM J. Matrix Anal. Appl., 24(1):260–280, 2002. doi:10.1137/S0895479801384937.
D. G. Meyer and S. Srinivasan. Balancing and model reduction for second-order form linear systems. IEEE Trans. Autom. Control, 41(11):1632–1644, 1996. doi:10.1109/9.544000.
Rachel Minster, Arvind K. Saibaba, Jishnudeep Kar, and Aranya Chakrabortty. Efficient algorithms for eigensystem realization using randomized svd. SIAM Journal on Matrix Analysis and Applications, 42(2):1045–1072, 2021. URL: https://epubs.siam.org/doi/10.1137/20M1327616, doi:10.1137/20M1327616.
D. Mustafa and K. Glover. Controller reduction by $\mathcal H_\infty $-balanced truncation. IEEE Trans. Autom. Control, 36(6):668–682, 1991. doi:10.1109/9.86941.
Jorge Nocedal and Stephen Wright. Numerical optimization. Springer Science & Business Media, 2006.
P. C. Opdenacker and E. A. Jonckheere. A contraction mapping preserving balanced reduction scheme and its infinity norm error bounds. IEEE Trans. Circuits Syst., 35(2):184–189, 1988. doi:10.1109/31.1720.
L. Peng and K. Mohseni. Symplectic model reduction of hamiltonian systems. SIAM Journal on Scientific Computing, 38(1):A1–A27, 2016. doi:10.1137/140978922.
G. Petrova & P. Wojtaszczyk R. DeVore. Greedy algorithms for reduced bases in banach spaces. Constructive Approximation, pages 455–466, 2013.
T. Reis and T. Stykel. Balanced truncation model reduction of second-order systems. Math. Comput. Model. Dyn. Syst., 14(5):391–406, 2008. doi:10.1080/13873950701844170.
Joost Rommes and Nelson Martins. Efficient computation of multivariable transfer function dominant poles using subspace acceleration. IEEE transactions on power systems, 21(4):1471–1483, 2006.
Lee J. Saibaba AK and Kitanidis PK. Randomized algorithms for generalized Hermitian eigenvalue problems with application to computing karhunen loeve expansion. Numerical Linear Algebra with Applications, 2016. doi:10.1002/nla.2026.
van BloemenWaanders B. Saibaba AK, Hart J. Randomized algorithms for generalized singular value decomposition with application to sensitivity analysis. Numerical Linear Algebra with Applications, 2021.
J. H. Tu, C. W. Rowley, D. M. Luchtenburg, S. L. Brunton, and J. N. Kutz. On dynamic mode decomposition: theory and applications. Journal of Computational Dynamics, pages 391–421, 2014.
Qian Wang, Jan S Hesthaven, and Deep Ray. Non-intrusive reduced order modeling of unsteady flows using artificial neural networks with application to a combustion problem. Journal of computational physics, 384:289–307, 2019.
S. Wyatt. Issues in Interpolatory Model Reduction: Inexact Solves, Second-order Systems and DAEs. PhD thesis, Virginia Polytechnic Institute and State University, Blacksburg, Virginia, USA, May 2012. URL: http://hdl.handle.net/10919/27668.
Y. Xu and T. Zeng. Optimal $\mathcal H_2$ model reduction for large scale MIMO systems via tangential interpolation. Int. J. Numer. Anal. Model., 8(1):174–188, 2011. URL: http://www.math.ualberta.ca/ijnam/Volume-8-2011/No-1-11/2011-01-10.pdf.
K. Zhou, G. Salomon, and E. Wu. Balanced realization and model reduction for unstable systems. Internat. J. Robust Nonlinear Control, 9(3):183–198, 1999. doi:10.1002/(SICI)1099-1239(199903)9:3<183::AID-RNC399>3.0.CO;2-E.