A Survey of Model Reduction Methods for Large-Scale Systems

By Athanasios C. Antoulas, Danny C. Sorensen, Serkan Gugercin. 2000

747 citations recorded by the source corpus.

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

View Paper: https://www.semanticscholar.org/paper/1db015756fe1877957ee4e6be73447f4aaf460e4

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Citations in the corpus

Model Reduction for fluids, Using Balanced Proper Orthogonal Decomposition (2005, methodology): “There are many other methods available for reducing both linear and nonlinear systems, and several of these are reviewed in [Antoulas et al., 2001].”
Stabilization of projection-based reduced order models for linear time-invariant systems via optimization-based eigenvalue reassignment (2014, background): “The first numerical example considered here involves a structural model of the Russian service module component of the international space station (ISS) [21].”
Handbook of Big Data (2016, methodology): “Model reduction: Model reduction [3] is used to produce a low-dimensional system that has the same response characteristics as the original system with far less storage requirements and much lower evaluation time.”
Analysis and Numerical Solution of Generalized Lyapunov Equations (2002, background): “The Lyapunov equations arise also in many other fields of control theory such as system balancing [102, 119], H∞ control [58, 176] and model reduction [4, 48, 119, 137, 150].”
Model reduction of large-scale systems by least squares (2006, methodology): “In this case the least-squares approximation becomes the Arnoldi procedure [8,4] for (A, b).”
Model Order Reduction for Linear and Nonlinear Systems: A System-Theoretic Perspective (2014, methodology): “Model reduction based on the cross-Gramian is also considered in [6,23,182].”
An adaptive-order rational Arnoldi method for model-order reductions of linear time-invariant systems (2006, methodology): “The Arnoldi method arises from the Hessenberg reduction A = V HV T for eigenvalue calculations [6,8,11,22].”
Balanced truncation model reduction for semidiscretized Stokes equation (2006, methodology): “There exist various model reduction approaches for standard (E = I) state space systems such as balanced truncation [18, 24, 32, 37, 38], singular perturbation approximation [22], optimal Hankel norm approximation [14], proper orthogonal decomposition [30, 39] and moment matching approximation [1, 1”
Balanced Truncation Model Reduction for Large-Scale Systems in Descriptor Form (2005, background): “Surveys on standard state space system approximation and model reduction can be found in [2, 3 , 28].”
H2 Model Reduction for Large-Scale Linear Dynamical Systems (2008, background): “Balanced truncation is well known as leading to small H∞ and H2 error norms, see [5, 17], mainly due to global information available through the usage of the two system gramians, the reachability and observability gramians, which are each solutions of a different Lyapunov equation.”
Interpolation among reduced‐order matrices to obtain parameterized models for design, optimization and probabilistic analysis (2009, methodology): “Projection-based model reduction methods derive a ROM by projecting the governing equations onto the subspace spanned by a set of basis vectors [3].”