# Bibliography¶

A05

A. C. Antoulas, Approximation of Large-Scale Dynamical Systems, SIAM, 2005.

ABG10

A. C. Antoulas, C. A. Beattie, S. Gugercin, Interpolatory model reduction of large-scale dynamical systems, Efficient Modeling and Control of Large-Scale Systems, Springer-Verlag, 2010.

BBKS18

P. Benner, Z. Bujanović, P. Kürschner, J. Saak, RADI: a low-rank ADI-type algorithm for large scale algebraic Riccati equations, Numerische Mathematik, Springer-Verlag, 2018.

BG09

C. A. Beattie, S. Gugercin, Interpolatory projection methods for structure-preserving model reduction, Systems & Control Letters 58, 2009

BG12

C. A. Beattie, S. Gugercin, Realization-independent H2-approximation, Proceedings of the 51st IEEE Conference on Decision and Control, 2012.

BKS11

P. Benner, M. Köhler, J. Saak, Sparse-Dense Sylvester Equations in $$\mathcal{H}_2$$-Model Order Reduction, Max Planck Institute Magdeburg Preprint, available from http://www.mpi-magdeburg.mpg.de/preprints/, 2011.

BCDDPW11

P. Binev, A. Cohen, W. Dahmen, R. DeVore, G. Petrova, P. Wojtaszczyk, Convergence rates for greedy algorithms in reduced basis methods, SIAM J. Math. Anal., 43(3), 2011.

BEOR14

A. Buhr, C. Engwer, M. Ohlberger, S. Rave, A Numerically Stable A Posteriori Error Estimator for Reduced Basis Approximations of Elliptic Equations, Proceedings of the 11th World Congress on Computational Mechanics, 2014.

BS18

A. Buhr, K. Smetana, Randomized Local Model Order Reduction. SIAM Journal on Scientific Computing, 40(4), A2120–A2151, 2018.

CLVV06

Y. Chahlaoui, D. Lemonnier, A. Vandendorpe, P. Van Dooren, Second-order balanced truncation, Linear Algebra and its Applications, 2006, 415(2–3), 373-384

DPW13

R. DeVore, G. Petrova & P. Wojtaszczyk, Greedy Algorithms for Reduced Bases in Banach Spaces, Constructive Approximation, 37, 455–466, 2013.

GP05

M. A. Grepl, A. T. Patera, A Posteriori Error Bounds For Reduced-Basis Approximations Of Parametrized Parabolic Partial Differential Equations, M2AN 39(1), 157-181, 2005.

GAB08

S. Gugercin, A. C. Antoulas, C. A. Beattie, $$\mathcal{H}_2$$ model reduction for large-scale linear dynamical systems, SIAM Journal on Matrix Analysis and Applications, 30(2), 609-638, 2008.

Haa17

Haasdonk, B., Reduced basis methods for parametrized PDEs - a tutorial introduction for stationary and instationary problems, in Model reduction and approximation, SIAM, Philadelphia, PA, 15, 65-136, 2017.

HDO11

Haasdonk, B.; Dihlmann, M. & Ohlberger, M., A training set and multiple bases generation approach for parameterized model reduction based on adaptive grids in parameter space, Math. Comput. Model. Dyn. Syst., 2011, 17, 423-442

HO08

B. Haasdonk, M. Ohlberger, Reduced basis method for finite volume approximations of parametrized evolution equations, M2AN 42(2), 277-302, 2008.

HMT11

N. Halko, P. G. Martinsson and J. A. Tropp, Finding structure with randomness: probabilistic algorithms for constructing approximate matrix decompositions, SIAM Review, 53(2), 217–288, 2011.

HLR18

C. Himpe, T. Leibner, S. Rave, Hierarchical Approximate Proper Orthogonal Decomposition, SIAM J. Sci. Comput. 40, A3267-A3292, 2018.

HPUU09

M. Hinze, R. Pinnau, M. Ulbrich, S. Ulbrich, Optimization with PDE constraints, Springer Netherlands, 2009.

HU18

J. Hesthaven, S. Ubbiali, Non-intrusive reduced order modeling of nonlinear problems using neural networks, Journal of Computational Physics, 363, pp. 55-78, 2018.

PK16

P. Kürschner, Efficient Low-Rank Solution of Large-Scale Matrix Equations, Shaker Verlag Aachen, available from http://pubman.mpdl.mpg.de/pubman/, 2016.

MS96

D. G. Meyer and S. Srinivasan, Balancing and model reduction for second-order form linear systems, IEEE Trans. Automat. Control, 1996, 41, 1632–1644

MG91

D. Mustafa, K. Glover, Controller Reduction by $$\mathcal{H}_\infty$$-Balanced Truncation, IEEE Transactions on Automatic Control, 36(6), 668-682, 1991.

NW06

J. Nocedal and S. J. Wright, Numerical optimization, Springer Series in Operations Research and Financial Engineering, Second Edition, Springer New-York, 2006

OJ88

P. C. Opdenacker, E. A. Jonckheere, A Contraction Mapping Preserving Balanced Reduction Scheme and Its Infinity Norm Error Bounds, IEEE Transactions on Circuits and Systems, 35(2), 184-189, 1988.

RL95

R. B. Lehoucq, Analysis and implementation of an implicitly restarted Arnoldi iteration, PhD thesis, Rice University, 1995

RS08

T. Reis and T. Stykel, Balanced truncation model reduction of second-order systems, Math. Comput. Model. Dyn. Syst., 2008, 14(5), 391-406

RM06

J. Rommes and N. Martins, Efficient computation of multivariable transfer function dominant poles using subspace acceleration. IEEE Trans. Power Syst. 21 (4), pp. 1471-1483, 2006

W12

S. Wyatt, Issues in Interpolatory Model Reduction: Inexact Solves, Second Order Systems and DAEs, PhD thesis, Virginia Tech, 2012

WHR19

Q. Wang, J. Hesthaven, D. Ray, Non-intrusive reduced order modeling of unsteady flows using artificial neural networks with application to a combustion problem, Journal of Computational Physics, 384, pp. 289-307, 2019.

XZ11

Y. Xu and T. Zeng, Optimal $$\mathcal{H}_2$$ Model Reduction for Large Scale MIMO Systems via Tangential Interpolation, International Journal of Numerical Analysis and Modeling, vol. 8, no. 1, pp. 174-188, 2011