Acta Numerica 2003: Model reduction methods based on Krylov subspaces

By R. Freund. 2003

378 citations recorded by the source corpus.

Subfields: Control and Systems Engineering, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/334b0b35bc942bb04f2bcc27c5e8afe676760036

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In Control and Systems Engineering

In Statistical and Nonlinear Physics

Citations in the corpus

A comparison of model reduction techniques from structural dynamics, numerical mathematics and systems and control (2013, background): “However, these reviews mainly focus on methods from the individual fields, i.e. they focus on methods from structural dynamics [11,13], systems and control [29] or numerical mathematics [4,22] only.”
Neurobiology of Aging: Contents (2005, neutral): “…2001) • mixed finite element approximations of elliptic PDEs (Brezzi 1974, Brezzi and Fortin 1991, Quarteroni and Valli 1994) • model order reduction for dynamical systems (Freund 2003, Heres and Schilders 2005, Stykel 2005) • optimal control (Battermann and Heinkenschloss 1998,…”
Recent computational developments in Krylov subspace methods for linear systems (2007, methodology): “Among the many topics not covered are the following (with some very limited pointers to the literature): the relation of Krylov subspace methods with orthogonal polynomials and Gaussian quadrature [115], [229], and with potential theory [85], [207]; special methods for model reduction [4], [21], [31”
Balanced truncation model reduction of second-order systems (2008, methodology): “Moment matching approximation based on Krylov subspace methods is one of the most used model reduction techniques for large-scale systems, see [5,6] for surveys on these methods.”
A Survey on Model Reduction of Coupled Systems (2008, methodology): “Such bases can be efficiently computed by a Lanczos or Arnoldi process [5, 20, 25] in the single-input single-output case and by Lanczos- or Arnoldi-type methods [22, 24, 30, 48] in the multi-input multi-output case.”
Model Order Reduction for Linear and Nonlinear Systems: A System-Theoretic Perspective (2014, methodology): “For survey papers on model reduction based on Krylov subspaces see, e.g. [ 11,77,88,89].”
A Survey of Projection-Based Model Reduction Methods for Parametric Dynamical Systems (2015, positive): “Surveys on this class of model reduction methods can be found in [22, 101]; see also [14, 15, 30, 44, 202].”
Data-driven operator inference for nonintrusive projection-based model reduction (2016, methodology): “There are also Krylov subspace methods, including multivariate Padé approximations and tangential interpolation [4, 5, 10].”
Survey of multifidelity methods in uncertainty propagation, inference, and optimization (2018, methodology): “There are also methods based on Krylov subspaces to generate a reduced basis [67, 75], including multivariate Pad\'e approximations and tangential interpolation for linear systems [13, 17, 74, 87].”
Efficient balancing-based MOR for large-scale second-order systems (2011, neutral): “Here, we will consider the application of fully automatic balancing-based MOR techniques.”
Closed-loop control of an open cavity flow using reduced-order models (2009, methodology): “It has thus been quickly realized that the application of approximate and iterative algorithms (as reviewed, for example, in Bai 2002 and Freund 2003), as well as the a priori reduction of the number of degrees of freedom (see e.g. Antoulas, Sorensen & Gugercin 2001), are crucial techniques when…”
Dimensional reduction of nonlinear finite element dynamic models with finite rotations and energy‐based mesh sampling and weighting for computational efficiency (2014, background): “Examples include the frequency-domain analysis of linear, time-invariant dynamical systems [1], the linear static analysis of problems where the underlying mathematical operators are affine in their parameter space [2], and problems with at most quadratic nonlinearities [3, 4].”
Parametric Order Reduction of Proportionally Damped Second Order Systems (2006, background): “The moments are defined as the negative coefficients of the Taylor series expansion of the transfer matrix [7].”