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

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.

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.

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.

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.

RS08

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

W12

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

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