H2 Model Reduction for Large-Scale Linear Dynamical Systems

By Serkan Gugercin, Athanasios C. Antoulas, Christopher A. Beattie. SIAM Journal on Matrix Analysis and Applications, 2008

660 citations recorded by the source corpus.

Subfields: Control and Systems Engineering, Statistical and Nonlinear Physics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/42ff8836bd8fffd0b8483e6e51debf64ddaeaf58

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Citations in the corpus

Model Reduction by Moment Matching for Linear and Nonlinear Systems (2010, background): “Alternatively, approximation errors expressed in terms of the or norm of the error system have been considered both in the linear case [9]‐[ 12 ] and in the nonlinear case [13].”
On two numerical methods for the solution of large-scale algebraic Riccati equations (2014, neutral): “, [1], [17], [16], [24], [25], [26], [31], [40], and references therein.”
Model reduction of dynamical systems on nonlinear manifolds using deep convolutional autoencoders (2018, methodology): “Common choices for computing the reduced-basis matrix Φ when the velocity is linear in its first argument include balanced truncation [52], rational interpolation [4, 31], the reduced-basis method [59, 64], Rayleigh–Ritz eigenvectors [20]; common choices when the velocity is nonlinear include POD [3”
A method to construct reduced‐order parameter‐varying models (2017, methodology): “Many studies use linear methods such as Krylov methods [32, 33].”
The AAA Algorithm for Rational Approximation (2016, methodology): “This method has had wide impact in the model reduction and related fields and has been extended in several directions since its original introduction by Gugercin, Antoulas, and Beattie [9, 26, 38].”
Survey of multifidelity methods in uncertainty propagation, inference, and optimization (2018, methodology): “We are here interested in richer and more heterogeneous sets of models, including projection-based reduced models [191, 181, 90, 21], data-fit interpolation and regression models [82, 80], machine-learning-based models such as support vector machines [201, 57, 39], and other simplified models [131, ”
Simulation process of flexible multibody systems with non-modal model order reduction techniques (2011, methodology): “based reduction methods clearly depends on the choice of expansion points sk. Recently in [ 28 ], a method was proposed where the H2-norm of the error H e is minimized if the moment matching conditions are chosen in an optimal way.”