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We present a novel reformulation of balanced truncation, a classical model reduction method.
SIAM J. Appl. Math. 16
Smith, R.: Matrix equation 𝐗𝐀 + 𝐁𝐗 = 𝐂 \mathbf{XA}+\mathbf{BX}=\mathbf{C} · 1968
Earlier work this paper cites.
Circuits and Systems, IEEE Transactions on 23
Mullis, C., Roberts, R.: Synthesis of minimum roundoff noise fixed point digital filters · 1976
Earlier work this paper cites.
In: Proceedings of 12th Asilomar Conference on Circuits, Systems & \& Computers, Pacific Grove, CA, 1978, pp. 705–714 (1978)
Kung, S.: A new identification and model reduction algorithm via singular value decomposition · 1978
Earlier work this paper cites.
IEEE Transactions on Automatic Control 26
Moore, B.: Principal component analysis in linear systems: Controllability, observability, and model reduction · 1981
Earlier work this paper cites.
Journal of computational physics 45
Boyd, J.P.: The optimization of convergence for chebyshev polynomial methods in an unbounded domain · 1982
Earlier work this paper cites.
Operator Theory: Advances and Applications 19
Curtain, R.F., Glover, K.: Balanced realisations for infinite dimensional systems · 1986
Earlier work this paper cites.
J. Sci. Comput 2
Boyd, J.P.: Exponentially convergent Fourier-Chebshev quadrature schemes on bounded and infinite intervals · 1987
Earlier work this paper cites.
BIT Numerical Mathematics 31
Sun, J.G.: Perturbation bounds for the Cholesky and QR factorizations · 1991
Earlier work this paper cites.
Systems & Control Letters 21
Scherpen, J.M.A.: Balancing for nonlinear systems · 1993
Earlier work this paper cites.
Prentice Hall, Inc. (1994)
Juang, J.: Applied system identification · 1994
Earlier work this paper cites.
Advances in Computational Mathematics 8
Penzl, T.: Numerical solution of generalized Lyapunov equations · 1998
Earlier work this paper cites.
SIAM J. Scientific Computing 21
Penzl, T.: A cyclic low-rank smith method for large sparse Lyapunov equations · 1999
Earlier work this paper cites.
SIAM (2002)
Higham, N.J.: Accuracy and stability of numerical algorithms · 2002
Earlier work this paper cites.
SIAM J. Matrix Analysis and Applications 24
Li, J.R., White, J.: Low rank solution of Lyapunov equations · 2002
Earlier work this paper cites.
J. of the Audio Engineering Society 50
Stan, G.B.V., Embrechts, J.J., Archambeau, D.: Comparison of different impulse response measurement techniques · 2002
Earlier work this paper cites.
AIAA Journal 40
Willcox, K., Peraire, J.: Balanced model reduction via the proper orthogonal decomposition · 2002
Earlier work this paper cites.
Numerical Algorithms 32
Gugercin, S., Sorensen, D.C., Antoulas, A.C.: A modified low-rank Smith method for large-scale Lyapunov equations · 2003
Earlier work this paper cites.
IEEE Trans. Comput. Aided Design Integr. Circuits Syst. 24
Phillips, J.R., Silveira, L.M.: Poor man’s TBR: a simple model reduction scheme · 2004
Earlier work this paper cites.
SIAM, Philadelphia (2005)
Antoulas, A.C.: Approximation of large-scale dynamical systems · 2005
Earlier work this paper cites.
Int. J. Bifurcat. Chaos 15
Rowley, C.W.: Model reduction for fluids, using balanced proper orthogonal decomposition · 2005
Earlier work this paper cites.
Linear Algebra and Its Applications 425
Mayo, A., Antoulas, A.: A framework for the solution of the generalized realization problem · 2007
Cited alongside, same era.
Ph.D. thesis, Rice University (2007)
Sabino, J.: Solution of large-scale Lyapunov equations via the block modified Smith method · 2007
Cited alongside, same era.
Mathematics of Computation 76
Weideman, J., Trefethen, L.: Parabolic and hyperbolic contours for computing the Bromwich integral · 2007
Cited alongside, same era.
Electron. Trans. Numer. Anal. (ETNA) 30
Stykel, T.: Low-rank iterative methods for projected generalized Lyapunov equations · 2008
Cited alongside, same era.
Intern. J. Computer Mathematics 86
Singler, J.R., Batten, B.A.: A proper orthogonal decomposition approach to approximate balanced truncation of infinite dimensional linear systems · 2009
Cited alongside, same era.
In: Proceedings of the 19th International Symposium on Mathematical Theory of Networks and Systems–MTNS, vol. 5 (2010)
SIAM J. Scientific Computing 37
Drmač, Z., Gugercin, S., Beattie, C.: Quadrature-based vector fitting for discretized ℋ 2 \mathcal{H}_{2} approximation · 2015
Later among the works it cites.
SIAM Journal on Scientific Computing 37
Drmač, Z., Gugercin, S., Beattie, C.: Vector fitting for matrix-valued rational approximation · 2015
Later among the works it cites.
Springer (2015)
Quarteroni, A., Manzoni, A., Negri, F.: Reduced basis methods for partial differential equations: an introduction, vol. 92 · 2015
Later among the works it cites.
SIAM J. Scientific Computing 38
Antoulas, A.C., Gosea, I.V., Ionita, A.C.: Model reduction of bilinear systems in the Loewner framework · 2016
Later among the works it cites.
SIAM J. Control and Optimization 54
Breiten, T.: Structure-preserving model reduction for integro-differential equations · 2016
Later among the works it cites.
Ph.D. thesis, Otto von Guericke Universität Magdeburg (2016)
Kürschner, P.: Efficient low-rank solution of large-scale matrix equations · 2016
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Benner, P., Schneider, A.: Balanced truncation model order reduction for LTI systems with many inputs or outputs · 2010
Cited alongside, same era.
SIAM J. on Control and Optimization 49
Benner, P., Damm, T.: Lyapunov equations, energy functionals and model order reduction of bilinear and stochastic systems · 2011
Cited alongside, same era.
SIAM Rev. 53
Halko, N., Martinsson, P.G., Tropp, J.A.: Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions · 2011
Cited alongside, same era.
Theoretical and Computational Fluid Dynamics 25
Ma, Z., Ahuja, S., Rowley, C.W.: Reduced-order models for control of fluids using the eigensystem realization algorithm · 2011
Cited alongside, same era.
IEEE Transactions on Automatic Control 57
Opmeer, M.R.: Model order reduction by balanced proper orthogonal decomposition and by rational interpolation · 2011
Cited alongside, same era.
In: 2012 IEEE 51st IEEE Conference on Decision and Control (CDC), pp. 4953–4958. IEEE (2012)
Beattie, C., Gugercin, S.: Realization-independent ℋ 2 \mathcal{H}_{2} -approximation · 2012
Cited alongside, same era.
GAMM Mitteilungen 36
Benner, P., Saak, J.: Numerical solution of large and sparse continuous time algebraic matrix Riccati and Lyapunov equations: A state of the art survey · 2013
Cited alongside, same era.
Later among the works it cites.
SIAM Review 58
Simoncini, V.: Computational methods for linear matrix equations · 2016
Later among the works it cites.
In: Model Reduction and Approximation. SIAM (2017)
Antoulas, A.C., Lefteriu, S., Ionita, A.C.: A tutorial introduction to the Loewner framework for model reduction (Chap. 8) · 2017
Later among the works it cites.
arXiv preprint available at https://arxiv.org/abs/1705.00160 (2017)
Benner, P., Goyal, P.: Balanced truncation model order reduction for quadratic-bilinear control systems · 2017
Later among the works it cites.
SIAM, Philadelphia, PA (2017)
Benner, P., Ohlberger, M., Cohen, A., Willcox, K.: Model Reduction and Approximation · 2017
Later among the works it cites.
SIAM J. Scientific Computing 39
Peherstorfer, B., Gugercin, S., Willcox, K.: Data-driven reduced model construction with time-domain Loewner models · 2017
Later among the works it cites.
NumAlgAppl 25
Gosea, I.V., Antoulas, A.C.: Data-driven model order reduction of quadratic-bilinear systems · 2018
Later among the works it cites.
Advances in Computational Mathematics 44
Gosea, I.V., Petreczky, M., Antoulas, A.C., Fiter, C.: Balanced truncation for linear switched systems · 2018
Later among the works it cites.
Algorithms 11
Himpe, C.: emgr · 2018
Later among the works it cites.
Linear Algebra and its Applications 537
Schulze, P., Unger, B., Beattie, C.A., Gugercin, S.: Data-driven structured realization · 2018
Later among the works it cites.
Computational Science and Engineering 21. SIAM, Philadelphia (2020)
Antoulas, A.C., Beattie, C., Gugercin, S.: Interpolatory methods for model reduction · 2020
Later among the works it cites.
arXiv preprint available at https://arxiv.org/abs/1903.05383 (2020)
Bertram, C., Faßbender, H.: Lyapunov and Sylvester equations: A quadrature framework · 2020
Later among the works it cites.
In: Model Reduction of Complex Dynamical Systems, pp. 119–139. Springer (2021)
Bertram, C., Faßbender, H.: A link between Gramian-based model order reduction and moment matching · 2021
Closest in time.
In: P. Benner, et al. (eds.) Model Reduction of Complex Dynamical Systems. Springer (2021)
Himpe, C.: Comparing (empirical-Gramian-based) model order reduction algorithms · 2021
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Pontes Duff, I.: (2021) · 2021
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