Approximation of large-scale dynamical systems: an overview

By Athanasios C. Antoulas, Danny C. Sorensen. 2004

465 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics, Numerical Analysis, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/cf8ce307ab9a3a862b6f159180685c35e97363c2

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Citations in the corpus

Mor4ansys: Generating compact models directly from ANSYS models (2004, methodology): “Consider for example the PDE for an elastic body f I + fD + fS = bu(t), (1) with f I the force caused by inertia, fD the damping force, fS the elastic force and bu(t) external forces depending on user input and varying in time [6].”
Efficient computation of transfer function dominant poles using subspace acceleration (2006, methodology): “A good survey on model reduction methods employing either singular value decompositions or moment matching-based methods is found in [9], [10].”
Reduced-basis methods applied to problems in elasticity : analysis and applications (2003, background): “Thus, as in certain other time-domain model-order-reduction methods [5, 45], the basis functions are “snapshots” of the solution at selected time instants; however, in [43] an ensemble of such series is constructed corresponding to different points in the non-time parameter domain D.”
Large-Population Cost-Coupled LQG Problems With Nonuniform Agents: Individual-Mass Behavior and Decentralized $\varepsilon$-Nash Equilibria (2007, background): “Techniques for dealing with various large-scale systems include model reduction, aggregation, and hierarchical optimization, just a few examples being [1], [7], [22], [28], and [29].”
Advances in deployable structures and surfaces for large apertures in space (2013, methodology): “Since model reduction per se is computationally quite costly as well, methods providing parameterized reduced models with explicit access to design parameters in the reduced model space are in order then, see for example Antoulas and Sorensen [85].”
Reinforcement Learning on Slow Features of High-Dimensional Input Streams (2010, methodology): “To understand the results, it is important to note that SFA is quite different from PCA or other more elaborate dimensionality reduction techniques [57,58].”
Analysis and Numerical Solution of Generalized Lyapunov Equations (2002, background): “Surveys on system approximation and model reduction can be found in [2, 4, 48, 121].”
Reduced--Basis Output Bound Methods for Parametrized Partial Differential Equations (2002, methodology): “Many reduction approaches based on Krylovsubspace techniques have been developed; for an overview see [7, 45] and the references contained therein.”
Model Order Reduction in Elastic Multibody Systems using the Floating Frame of Reference Formulation (2012, methodology): “Furthermore, in Antoulas and Sorensen (2001) the value σn+1 σ1 < τ (26)”
Krylov subspace techniques for reduced-order modeling of large-scale dynamical systems (2002, methodology): “They sometimes are also called Gramian-based model reduction methods, or SVD-based model reduction methods [86,3].”
Gramian-Based Reduction Method Applied to Large Sparse Power System Descriptor Models (2008, methodology): “The balanced truncation technique requires the computation of the system controllability and observability gramians [9], [12], [18].”
Efficient Computation of Multivariable Transfer Function Dominant Poles Using Subspace Acceleration (2006, methodology): “A survey on model reduction methods employing either singular value decompositions or moment matching based methods is found in [8,9].”